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

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+135x^88+440x^92+1024x^93+256x^94+119x^96+72x^100+1x^184

The gray image is a linear code over GF(2) with n=744, k=11 and d=352.
This code was found by Heurico 1.16 in 1.17 seconds.