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  X  1  1  1  1  1  1  1  1  1  1  1  1  1  X  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  1  1  1  1  1  1  1  1  1  1 X^2  1  1  X
 0 X^3+X^2  0 X^2  0  0 X^2 X^3+X^2  0  0 X^2 X^3+X^2  0  0 X^2 X^3+X^2  0  0 X^2 X^3+X^2  0  0 X^2 X^3+X^2  0  0 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  0 X^2 X^3+X^2  0  0 X^2 X^2  0 X^3 X^2 X^3  0 X^2 X^3 X^3+X^2 X^2 X^3  0  0 X^3+X^2 X^3+X^2  0 X^2 X^3+X^2 X^3+X^2  0  0 X^3+X^2 X^2 X^3 X^3+X^2 X^3 X^3 X^3 X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^3 X^3 X^3 X^3+X^2 X^2 X^3  0 X^3 X^2 X^3+X^2 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^2 X^3  0 X^3+X^2
 0  0 X^3+X^2 X^2  0 X^3+X^2 X^2  0 X^3+X^2  0 X^2  0  0 X^3+X^2 X^2  0  0 X^3+X^2 X^2  0  0 X^3+X^2 X^2  0  0 X^3+X^2 X^2 X^3  0 X^2 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^3 X^3+X^2 X^3 X^2 X^3+X^2 X^3 X^3 X^2 X^3+X^2  0 X^3 X^2  0 X^2 X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^3 X^2  0 X^2 X^2 X^3+X^2 X^2 X^3 X^3 X^3 X^3+X^2 X^3 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3 X^3  0  0  0 X^3+X^2 X^2  0 X^2 X^3+X^2  0 X^2  0 X^3+X^2 X^3 X^3+X^2  0 X^2 X^3
 0  0  0 X^3  0  0 X^3  0  0  0 X^3  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3  0  0  0  0  0  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3  0  0  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0  0  0  0 X^3
 0  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0  0 X^3  0  0  0 X^3  0  0 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0  0 X^3  0 X^3  0  0  0  0 X^3  0 X^3  0 X^3  0  0 X^3  0  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0  0  0  0  0  0  0 X^3 X^3
 0  0  0  0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0 X^3  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0  0 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 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+111x^92+76x^94+612x^96+512x^97+540x^98+132x^100+20x^102+25x^104+4x^106+13x^108+1x^112+1x^184

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 145 seconds.