The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 X X 1 X X 1
0 2X 0 0 0 0 0 0 0 0 0 0 0 0 0 2X 0 2X 2X 0 0 2X 2X 0 2X 2X 0 2X 0 2X 2X 0 2X 0 0 2X 2X 2X 2X 0 2X 2X 2X 0 2X 2X 0 0 2X 0 2X 2X 2X 2X 0 0 0 0 2X 2X 0 0 0 0 0 2X 2X 2X 2X 0 2X 2X 0 0 0 0 2X 2X 2X 2X 0 2X 0 0 0
0 0 2X 0 0 0 0 0 0 0 0 0 0 0 0 2X 2X 2X 0 0 2X 2X 0 2X 2X 0 0 0 2X 2X 2X 2X 0 2X 0 0 2X 2X 0 2X 0 2X 0 2X 2X 2X 2X 0 2X 2X 2X 0 0 2X 0 0 2X 0 0 0 2X 2X 0 0 2X 2X 0 0 2X 2X 0 0 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0
0 0 0 2X 0 0 0 0 0 0 0 0 0 0 0 2X 2X 0 2X 2X 2X 0 0 0 2X 2X 2X 2X 2X 2X 0 0 0 0 2X 0 2X 0 2X 2X 2X 2X 0 0 0 2X 2X 2X 0 2X 0 2X 0 2X 2X 2X 0 0 2X 0 2X 0 0 2X 2X 2X 2X 0 0 2X 0 2X 0 0 0 2X 0 2X 2X 0 2X 0 0 2X 0
0 0 0 0 2X 0 0 0 0 0 0 0 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 2X 0 0 0 2X 0 2X 0 2X 2X 0 0 2X 2X 2X 2X 2X 0 0 0 0 0 2X 2X 2X 0 2X 0 0 0 0 2X 2X 0 0 2X 2X 0 2X 2X 2X 2X 2X 0 2X 2X 2X 0 0 0 2X 0 0 0
0 0 0 0 0 2X 0 0 0 2X 2X 2X 2X 2X 0 0 0 0 0 0 2X 2X 0 0 2X 2X 0 0 0 2X 2X 0 0 2X 0 2X 2X 0 2X 2X 2X 2X 0 0 0 2X 0 2X 0 2X 2X 2X 2X 0 2X 0 0 0 0 0 0 2X 2X 0 2X 0 2X 2X 0 2X 0 0 0 2X 0 2X 2X 0 2X 2X 0 0 2X 0 2X
0 0 0 0 0 0 2X 0 2X 2X 2X 0 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 0 0 0 0 0 2X 0 0 2X 2X 0 2X 2X 0 2X 0 0 2X 2X 0 0 0 2X 2X 0 0 2X 0 2X 0 2X 0 0 0 2X 2X 2X 2X 0 0
0 0 0 0 0 0 0 2X 2X 0 2X 2X 0 2X 2X 0 0 0 0 2X 2X 0 0 2X 0 2X 0 0 2X 2X 0 0 2X 2X 0 0 0 0 2X 2X 0 2X 2X 0 2X 0 2X 0 2X 2X 2X 0 0 0 2X 2X 0 0 2X 0 2X 2X 0 0 0 2X 2X 2X 2X 0 0 0 2X 0 2X 2X 0 0 0 2X 2X 2X 2X 0 2X
generates a code of length 85 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 78.
Homogenous weight enumerator: w(x)=1x^0+49x^78+72x^80+40x^82+80x^84+1536x^85+127x^86+84x^88+8x^90+31x^94+18x^96+1x^102+1x^160
The gray image is a code over GF(2) with n=680, k=11 and d=312.
This code was found by Heurico 1.16 in 0.906 seconds.