The generator matrix

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

generates a code of length 97 over Z2[X]/(X^4) who´s minimum homogenous weight is 94.

Homogenous weight enumerator: w(x)=1x^0+384x^94+264x^95+484x^96+32x^97+320x^98+176x^99+254x^100+32x^101+56x^102+8x^103+26x^104+1x^108+8x^110+1x^124+1x^144

The gray image is a linear code over GF(2) with n=776, k=11 and d=376.
This code was found by Heurico 1.16 in 42.2 seconds.