The generator matrix

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

generates a code of length 94 over Z2[X]/(X^4) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+252x^88+40x^89+292x^90+120x^91+339x^92+608x^93+866x^94+608x^95+324x^96+120x^97+234x^98+40x^99+143x^100+78x^102+26x^104+2x^106+2x^108+1x^168

The gray image is a linear code over GF(2) with n=752, k=12 and d=352.
This code was found by Heurico 1.16 in 16.3 seconds.