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  1  1  1  X  X  1
 0  X  0 X^2+X X^2 X^3+X^2+X X^3+X^2  X X^2 X^2+X X^3 X^3+X  0 X^2+X X^2  X  0 X^2+X X^3+X^2 X^3+X X^3 X^3+X^2+X X^2  X X^3 X^3+X^2+X X^2  X X^2  X X^3 X^3+X^2+X  0 X^2+X  0 X^2+X X^2  X X^3+X^2 X^3+X  0 X^2+X  0 X^2+X X^2  X X^2  X X^3+X^2 X^3+X X^3+X^2 X^3+X X^2  X X^3+X^2 X^3+X  0 X^3 X^2+X X^3+X^2+X X^3 X^3+X^2+X  0 X^2+X  0 X^3 X^3  0 X^2+X X^3+X^2+X X^3+X^2+X X^2+X X^2  X  0 X^3+X^2+X X^3 X^3+X^2+X  0 X^3+X X^3+X^2 X^2+X X^3+X^2 X^3+X^2+X X^3 X^3+X^2 X^3 X^3+X X^3+X^2+X X^3+X X^3+X^2+X X^3+X^2 X^3
 0  0 X^3+X^2  0 X^2 X^2  0 X^2 X^3+X^2  0 X^2  0  0 X^3+X^2  0 X^3+X^2 X^3 X^3 X^3 X^3 X^2 X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^3 X^3 X^2 X^2 X^3+X^2 X^3+X^2  0  0 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3  0  0  0 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3  0 X^3+X^2 X^3  0 X^2  0 X^3 X^2 X^3+X^2 X^3 X^2 X^3 X^2 X^3 X^3 X^2 X^2 X^3 X^3 X^2 X^2 X^3 X^3 X^2 X^2 X^3+X^2 X^2 X^3  0 X^3 X^3+X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3+X^2  0 X^2 X^3  0 X^3+X^2 X^3+X^2 X^2
 0  0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0  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  0 X^3 X^3  0  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0  0 X^3 X^3  0  0 X^3  0 X^3  0  0  0 X^3 X^3 X^3  0 X^3  0  0
 0  0  0  0 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 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  0 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0 X^3  0 X^3  0  0 X^3  0 X^3 X^3  0  0  0  0 X^3  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+57x^88+52x^89+121x^90+80x^91+282x^92+912x^93+284x^94+56x^95+64x^96+28x^97+73x^98+24x^99+11x^100+2x^102+1x^180

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 1.44 seconds.