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

generates a code of length 91 over Z2[X]/(X^4) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+216x^87+638x^88+768x^89+656x^90+304x^91+402x^92+328x^93+240x^94+112x^95+116x^96+128x^97+88x^98+56x^99+30x^100+8x^101+3x^104+2x^108

The gray image is a linear code over GF(2) with n=728, k=12 and d=348.
This code was found by Heurico 1.16 in 6.41 seconds.