The generator matrix

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

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+230x^86+696x^87+682x^88+554x^89+436x^90+368x^91+346x^92+178x^93+194x^94+140x^95+74x^96+128x^97+49x^98+16x^99+1x^100+1x^102+1x^110+1x^118

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 0.515 seconds.