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  X  1  1  1  0  X  1 X^2  1
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X  0 X^2+X X^3+X X^3+X^2 X^3 X^3+X^2+X X^2 X^3+X  0 X^2+X X^3+X X^3+X^2 X^2+X  0 X^3+X X^3+X^2  0 X^2+X X^3+X X^3+X^2 X^3 X^3+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^2+X  0 X^3+X^2 X^3+X X^3 X^3+X^2+X X^2  X  0 X^2+X  0 X^2+X X^3 X^3+X^2+X X^3 X^3+X^2+X X^3+X^2 X^3+X X^3+X^2 X^3+X X^2  X X^2  X  0 X^2+X  0 X^3 X^3 X^2+X X^3+X^2+X X^3+X^2+X X^3+X^2 X^2 X^3+X^2 X^2+X X^3+X^2+X  X X^2 X^3+X X^3+X X^2+X X^3+X^2+X  X X^2+X X^3  0 X^3  X X^2+X X^3+X^2+X X^3+X^2 X^2+X
 0  0 X^3  0  0  0 X^3  0  0  0  0 X^3  0  0 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0  0  0 X^3  0 X^3  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  0  0 X^3 X^3 X^3 X^3  0  0  0
 0  0  0 X^3  0  0  0 X^3  0  0  0  0  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 X^3  0 X^3  0  0 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 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0 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 X^3 X^3 X^3  0 X^3 X^3  0  0  0  0
 0  0  0  0 X^3  0 X^3  0  0 X^3 X^3 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 X^3  0  0 X^3  0  0  0  0  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0  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  0 X^3 X^3 X^3  0  0 X^3  0  0 X^3  0  0  0  0  0  0 X^3
 0  0  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0  0  0  0  0  0 X^3 X^3 X^3  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  0  0 X^3 X^3  0  0 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0  0  0  0  0  0 X^3  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+30x^88+150x^89+146x^90+38x^91+382x^92+468x^93+504x^94+84x^95+57x^96+150x^97+21x^98+6x^99+10x^100+1x^178

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 1.08 seconds.