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

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+124x^88+240x^92+1280x^94+349x^96+16x^100+27x^104+10x^112+1x^168

The gray image is a linear code over GF(2) with n=752, k=11 and d=352.
This code was found by Heurico 1.16 in 30.3 seconds.