The generator matrix

 1  0  1  1 X^2  1  1  1 X^2+X  1  1  0 X^3+X  1  1  1  1 X^2 X^3  1  1  1  1 X^3  1  1  X  1  1 X^2+X  1  X  1  1  1  1 X^2+X  1  1  1 X^2+X X^3+X  1  1 X^2  1  1  1  1  1 X^2 X^2  1  1  1  1  1  1  1  1  1  1  1  1 X^3+X X^3+X  1 X^2+X X^3+X^2  1  1  1 X^2  1 X^3 X^3  1  1  1  1 X^3  1  1  1  X X^3 X^3+X^2+X  1 X^2  X
 0  1  1 X^2+X  1 X^2+X+1 X^2 X^3+1  1 X+1 X^3+X^2+X  1  1  0 X^3+X^2+1 X^3 X^3+1  1  1  X X+1 X^2+X X^3+X+1  1 X^2 X^2+1  1 X^3+X^2+X+1 X^3+X^2  1 X^2+1  1 X^3 X^3+X^2+X X+1  X  1 X^2+X+1 X^2+1 X^3+X^2+X  1  1 X^2+X+1 X^2  1 X^3+1 X^3+X^2+X+1 X^3+X^2+X  1 X^3+X  1  X  0 X^3+X^2 X^2+1 X^3+1 X+1 X+1 X^2+X X^3+X+1 X^3+X^2+X+1  X  X X+1  1  1 X^2  1  1 X^3 X^3+X X^3+X^2  1 X^2+1  0  1  0 X^3+X^2+1  X X^3+X  1 X^2+1 X^2+X X^3+1 X^3+X  1  1  1  1 X^3+X^2
 0  0  X  0 X^3+X  X X^3+X X^3  0 X^3 X^3+X X^3+X^2+X X^2 X^3+X^2 X^3+X^2 X^3+X^2+X X^3+X^2+X X^2+X X^3+X X^2 X^2+X X^2+X X^2 X^2 X^2 X^2+X  X X^3+X^2 X^2+X X^3+X^2  X  X X^3+X X^3+X X^3+X^2+X X^3 X^3+X^2+X  X  0 X^3+X^2+X X^2+X X^3 X^3+X^2 X^2 X^3  0 X^3 X^2 X^2  0 X^2 X^3+X^2+X X^3 X^3 X^2 X^3+X^2+X  X X^3  0  0 X^3+X^2+X X^3+X X^3+X^2+X X^3+X^2 X^2 X^2+X X^3+X^2+X X^3 X^3+X^2+X X^2 X^2  X  0 X^3+X^2  X X^3+X X^3 X^3+X  X X^3+X^2 X^3+X^2+X  0 X^3+X X^2 X^3+X X^2+X X^3+X X^3+X^2 X^3+X^2 X^3+X^2+X
 0  0  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0  0 X^3  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0  0 X^3  0  0  0  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+683x^86+152x^87+856x^88+120x^89+730x^90+128x^91+680x^92+64x^93+456x^94+40x^95+123x^96+8x^97+22x^98+29x^102+1x^104+2x^112+1x^120

The gray image is a linear code over GF(2) with n=720, k=12 and d=344.
This code was found by Heurico 1.16 in 3.66 seconds.