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

generates a code of length 93 over Z2[X]/(X^4) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+197x^88+284x^89+528x^90+392x^91+559x^92+344x^93+476x^94+392x^95+428x^96+196x^97+190x^98+48x^99+40x^100+8x^101+4x^102+3x^104+2x^112+2x^114+1x^132+1x^136

The gray image is a linear code over GF(2) with n=744, k=12 and d=352.
This code was found by Heurico 1.16 in 1.27 seconds.