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

generates a code of length 97 over Z2[X]/(X^4) who´s minimum homogenous weight is 92.

Homogenous weight enumerator: w(x)=1x^0+94x^92+176x^94+144x^95+403x^96+480x^97+386x^98+144x^99+117x^100+52x^102+28x^104+10x^106+12x^108+1x^180

The gray image is a linear code over GF(2) with n=776, k=11 and d=368.
This code was found by Heurico 1.16 in 1.36 seconds.