The generator matrix

 1  0  1  1  1  X  1  1 X^2+X  1  1  X X^3+X^2+X  1  1 X^3+X^2  1  1  0  1  1  1 X^2  1  1  1  1  1 X^2+X  1  1 X^3+X  1  1 X^2 X^3+X^2+X  1  1  1  1  1  1  1  1 X^2 X^2  X  1 X^3  X X^3+X^2  0 X^3 X^3+X  1 X^3  0 X^3+X^2+X X^3+X X^2+X X^3+X^2 X^3  1  0 X^3+X^2+X  1 X^3+X^2 X^2+X X^3+X^2+X  1  1  1  1  1  X  1  0  1  1  1  1 X^2+X  1  1  0  1  1 X^3+X  X  1  1  1  1
 0  1  1 X^2 X+1  1  X X^3+1  1 X^2+X X^3+X+1  1  1  0 X^3+X^2+X+1  1 X^3+X^2 X^2+X+1  1 X^2+1 X^2+X X^3+X^2+X  1 X^3+X^2+1 X^3 X^3+X^2 X^3+X X^3+X  1 X^2+X+1 X+1  1 X^3+X^2+1 X^3+1  1  1  X X^2+1  1 X^3+X^2 X^3+X^2+X X^3+X^2+X+1  0 X^3+X+1  1  1  1 X^3  1  X  1  0  1  1 X+1  1  1  1  1  1  1  X X^3  1  1 X^2+X  1  1  1 X^3+X^2 X^2+X  X X^3+X X^2 X^2+X X^3+X  1 X^3+X X^2 X^3+X^2+X X^3+X^2+X  1 X^3+X^2 X^2+X  X X^2+X X^2+1  1  1 X^3 X^3 X^2  0
 0  0  X X^3+X X^3 X^3+X X^3+X X^3  0  0  X X^2+X X^3+X^2 X^3+X^2 X^3+X^2+X X^2+X X^2+X X^2 X^3+X^2 X^2+X X^2 X^3+X X^3+X X^3+X^2  X X^3  0 X^3+X^2+X X^2+X X^3+X X^2  0  X X^2 X^2  X X^3+X^2 X^3 X^3+X^2+X X^2 X^2+X  0 X^2+X X^3+X^2+X X^3 X^2+X X^3+X^2 X^2  X X^3+X  X  X X^3+X^2+X X^2 X^3+X^2 X^2+X X^3+X X^3+X^2+X X^3  X  0 X^2 X^3+X^2+X X^2 X^2+X X^3 X^3 X^2 X^3+X  0 X^2+X  X X^3+X^2  X X^3+X^2+X X^3 X^3 X^2 X^3 X^3+X^2+X X^3 X^3 X^3+X  X X^2+X X^3+X X^2  X  0 X^3+X X^2+X X^2  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+32x^89+306x^90+358x^91+332x^92+296x^93+212x^94+162x^95+136x^96+70x^97+62x^98+32x^99+24x^100+2x^101+12x^102+4x^103+1x^104+4x^107+1x^108+1x^140

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 2.05 seconds.