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

generates a code of length 90 over Z2[X]/(X^4) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+21x^82+41x^84+35x^86+94x^88+256x^89+1180x^90+256x^91+87x^92+22x^94+15x^96+13x^98+15x^100+7x^102+2x^104+2x^106+1x^172

The gray image is a linear code over GF(2) with n=720, k=11 and d=328.
This code was found by Heurico 1.16 in 0.75 seconds.