The generator matrix

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

generates a code of length 97 over Z2[X]/(X^4) who´s minimum homogenous weight is 93.

Homogenous weight enumerator: w(x)=1x^0+72x^93+285x^94+336x^95+310x^96+274x^97+198x^98+176x^99+168x^100+106x^101+83x^102+24x^103+8x^104+4x^107+1x^108+1x^130+1x^142

The gray image is a linear code over GF(2) with n=776, k=11 and d=372.
This code was found by Heurico 1.16 in 3.3 seconds.