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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X X^2+X  0 X^3+X X^3+X^2 X^3 X^3+X X^2 X^2+X X^3+X^2+X  0 X^3+X^2 X^3+X  0 X^2+X X^3+X^2 X^3+X  0 X^2+X X^3+X^2 X^3+X  0 X^2+X X^3+X^2 X^3+X X^3 X^3+X^2+X X^2  X X^3 X^3+X^2+X X^2  X  0 X^2+X X^3 X^3+X^2+X X^3+X^2 X^3+X X^2  X X^3+X^2 X^2+X X^3+X^2+X X^2 X^3+X^2 X^2+X X^2 X^3+X^2+X  0  0 X^3 X^3+X X^3+X  X X^3  X  0 X^2+X  0 X^3 X^3 X^2+X X^3+X^2+X X^3+X^2+X  0 X^3 X^2+X X^3+X^2+X X^3+X^2 X^3+X X^3+X^2 X^3 X^2 X^2+X  X X^3+X  0 X^3+X^2+X  X X^3+X  X X^2+X
 0  0 X^3  0  0  0 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3  0  0  0 X^3  0  0  0  0  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0
 0  0  0 X^3  0  0  0  0  0  0  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0  0 X^3 X^3  0 X^3  0
 0  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3  0  0 X^3  0  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0
 0  0  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0 X^3 X^3  0  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3

generates a code of length 90 over Z2[X]/(X^4) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+66x^85+70x^86+74x^87+47x^88+52x^89+1428x^90+52x^91+47x^92+74x^93+70x^94+66x^95+1x^180

The gray image is a linear code over GF(2) with n=720, k=11 and d=340.
This code was found by Heurico 1.16 in 0.953 seconds.