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  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  1  1  1  X  1  1 X^3+X^2  1  1
 0  X  0  X X^3 X^3 X^3+X X^3+X X^2 X^2+X X^2 X^2+X X^3+X^2 X^3+X^2+X X^3+X^2 X^3+X^2+X  0  X X^2 X^2+X X^3 X^3+X X^2 X^2+X X^3 X^3+X X^3+X^2+X X^2 X^3 X^2+X X^3+X^2  X X^2+X  0 X^3 X^3+X^2+X X^3 X^3+X^2 X^3+X X^3+X X^2 X^3+X X^2 X^3+X^2+X X^3+X^2 X^3  X X^2+X X^3+X^2+X X^3+X X^3+X^2 X^3+X^2  0 X^3+X^2+X X^3+X  0 X^3+X X^3 X^2+X X^3+X^2+X X^3+X^2  X X^3 X^3+X^2 X^3+X^2  0  X X^3+X X^3 X^3+X^2+X X^3+X^2+X  0 X^3+X^2 X^3  X  0 X^2+X X^2+X X^2+X X^2 X^2 X^3+X^2 X^3+X X^2+X  X X^3+X X^3+X^2  X X^2 X^3+X^2 X^2+X X^3+X  0 X^3+X  X  X X^3
 0  0  X  X X^2 X^3+X^2+X X^2+X X^3+X^2 X^2 X^2+X  X  0  0  X X^3+X^2+X X^3+X^2  0  X  X  0 X^2 X^2+X X^3+X^2+X X^3+X^2 X^2+X X^3 X^3+X X^3+X^2 X^3+X X^3+X^2+X X^3 X^2 X^2 X^3+X^2+X  0 X^3+X^2+X  X X^2 X^3 X^3+X X^3+X^2+X X^3+X^2+X X^3  0  X X^3+X^2 X^3+X^2 X^3+X X^2+X X^3+X^2  0  X X^3+X^2 X^3 X^3+X X^2+X X^3+X^2+X X^3+X  X X^2 X^2  0 X^3 X^2+X X^3+X^2+X X^3 X^3+X^2  0 X^3+X^2  X X^2+X X^2+X X^3+X^2 X^3 X^3+X X^3+X^2+X X^3+X^2 X^3+X X^3 X^3+X  0 X^3+X  X X^3+X^2+X X^2  0 X^3 X^3+X^2+X X^2+X X^3+X^2 X^2 X^2+X X^3+X  X X^3 X^3+X  X
 0  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0  0 X^3  0  0  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0 X^3  0  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3  0  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0  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+106x^93+99x^94+162x^95+284x^96+760x^97+288x^98+136x^99+90x^100+110x^101+4x^102+6x^103+1x^104+1x^190

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 1.24 seconds.