The generator matrix

 1  0  1  1  1 X^2+X  1 X^3+X^2  1  1  1 X^3+X  1  1 X^3  1 X^3+X^2+X  1  1  1 X^2  1  1  X  1  1  0  1 X^2+X  1  1  0  1  1 X^2+X  1  1  X  1  1 X^2  1  1 X^2  1  1  X  1  X  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^3  1  1 X^3+X^2+X  0  1  1  1 X^3+X  1  1 X^3  1 X^3  1  1  1  X  X  1  1 X^3
 0  1 X+1 X^2+X X^2+1  1 X^3+1  1 X^3+X^2 X+1 X^3+X  1 X^3+X^2+X+1 X^3  1 X^3+X^2+X  1 X^3+X^2+1 X^2+X+1 X^2  1  X  1  1  0 X+1  1 X^2+X  1 X^3+X^2+X+1 X^3+X^2+1  1  0  X  1 X^3+X+1  1  1 X^2 X^2+X  1 X^3+X^2+X+1 X^2  1 X^2+1  X  1 X^3+1  X  X X^2+1 X^2+X+1 X^2+1 X^3+X^2+X+1  1 X^3+X+1  1 X+1 X^3+X^2+1 X^2+X+1 X+1 X^3+1 X^3+X^2+1 X^3+1 X^3+X+1 X^3+X+1 X^3+X+1  1  1 X^3 X^3+X^2+X  1  1 X^3+X^2 X^2+1 X^3+X  1 X^3+X+1 X^3+X+1 X^2  1  1 X^3+X^2+X+1 X^3+X X^3+X+1 X^3  1 X^2+X+1 X^3+X^2  1
 0  0 X^2  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2  0 X^3  0  0  0 X^3 X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2  0  0 X^3  0  0 X^3 X^3+X^2 X^3 X^3+X^2 X^3  0 X^2 X^2 X^2 X^3 X^3+X^2 X^3 X^3+X^2 X^3  0 X^3+X^2 X^3+X^2 X^3  0  0 X^2 X^3+X^2 X^2 X^2 X^3+X^2  0 X^3 X^3+X^2  0 X^3  0 X^2 X^2  0 X^3  0 X^3 X^3 X^3+X^2 X^2 X^3+X^2 X^2 X^2
 0  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0  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  0  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0 X^3  0  0  0  0  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0
 0  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0  0  0  0  0  0  0  0  0  0 X^3  0  0 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  0 X^3  0  0 X^3 X^3  0  0 X^3  0  0  0 X^3 X^3  0 X^3 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+132x^85+328x^86+606x^87+328x^88+604x^89+455x^90+430x^91+232x^92+442x^93+254x^94+146x^95+22x^96+34x^97+31x^98+34x^99+8x^100+2x^101+1x^102+2x^105+2x^106+1x^126+1x^128

The gray image is a linear code over GF(2) with n=720, k=12 and d=340.
This code was found by Heurico 1.16 in 1.14 seconds.