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

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+174x^94+106x^95+176x^96+176x^97+142x^98+100x^99+110x^100+2x^102+2x^103+32x^104+1x^120+1x^126+1x^134

The gray image is a linear code over GF(2) with n=776, k=10 and d=376.
This code was found by Heurico 1.16 in 1.56 seconds.