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

generates a code of length 90 over Z2[X]/(X^4) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+135x^86+102x^87+150x^88+228x^89+880x^90+224x^91+120x^92+68x^93+78x^94+10x^95+25x^96+8x^97+18x^98+1x^174

The gray image is a linear code over GF(2) with n=720, k=11 and d=344.
This code was found by Heurico 1.16 in 0.938 seconds.