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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  X  X  1  X
 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 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3 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  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0  0  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0  0 X^3
 0  0 X^3  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0  0 X^3  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3
 0  0  0 X^3  0  0  0  0  0  0  0  0  0  0  0  0  0  0 X^3 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3  0 X^3  0  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0  0  0  0 X^3 X^3  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  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0  0  0 X^3  0 X^3 X^3  0  0  0  0  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0  0 X^3 X^3  0  0  0 X^3  0 X^3 X^3  0 X^3  0
 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 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0  0  0  0 X^3  0 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0  0 X^3
 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  0  0  0  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0  0  0 X^3 X^3  0  0  0 X^3  0  0  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  0  0  0  0  0  0  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0  0  0  0 X^3 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 86.

Homogenous weight enumerator: w(x)=1x^0+45x^86+71x^88+40x^90+80x^92+1536x^93+135x^94+86x^96+8x^98+27x^102+17x^104+1x^110+1x^176

The gray image is a linear code over GF(2) with n=744, k=11 and d=344.
This code was found by Heurico 1.16 in 1.14 seconds.