The generator matrix

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

generates a code of length 93 over Z2[X]/(X^4) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+204x^89+199x^90+192x^91+288x^92+312x^93+285x^94+180x^95+157x^96+180x^97+26x^98+20x^99+1x^100+1x^110+1x^116+1x^138

The gray image is a linear code over GF(2) with n=744, k=11 and d=356.
This code was found by Heurico 1.16 in 1.03 seconds.