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  0  1  1  1  1  1 X^3  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  X  X X^2  0 X^3+X^2  X X^3 X^2  X  X  X  X  X X^2  X  0 X^3  X X^2 X^3 X^3 X^3+X^2  X  X  0 X^2 X^3  X  1
 0  X  0  X  0  0  X  X X^2 X^2+X X^2 X^2+X X^2 X^2 X^2+X X^2+X  0  0  X  X  0  0  X  X X^2 X^2 X^2+X X^3 X^2+X X^2 X^2 X^2+X X^2+X X^3 X^3 X^3 X^3+X X^3+X X^3+X^2 X^3+X^2 X^3+X^2+X X^3+X^2+X X^3 X^3 X^3+X X^3+X X^3+X^2 X^3+X^2 X^3+X^2+X X^3+X^2+X X^3 X^3 X^3+X X^3+X X^3 X^3 X^3+X X^3+X X^3+X^2 X^3+X^2 X^3+X^2+X X^3+X^2+X X^3+X^2 X^3+X^2 X^3+X^2+X X^3+X^2+X  X X^2+X  X X^3+X^2+X X^2  X  X X^2  X  X X^3+X^2 X^3+X X^3+X^2+X X^3+X X^2+X X^3+X^2  0  0  X X^3  X X^2  X  X X^3+X^2  0 X^3+X^2  0  0 X^3+X^2  0
 0  0  X  X X^3+X^2 X^2+X X^3+X^2+X X^2 X^2 X^2+X X^3+X X^3 X^3+X^2+X X^3 X^3+X X^3+X^2 X^3 X^3+X^2+X X^3+X X^3+X^2 X^3+X X^2 X^2+X X^3 X^3+X^2  X X^3+X^2+X  X  0  0 X^2+X  X X^2  X X^3 X^3+X^2+X X^3+X X^3+X^2 X^3+X^2 X^3+X X^3+X^2+X X^3 X^2  X X^2+X  0  0 X^2+X  X X^2  0 X^2+X X^3+X^2+X X^3 X^3+X^2 X^3+X  X X^2 X^2  X X^2+X  0 X^3 X^3+X^2+X X^3+X X^3+X^2  X  0 X^3+X^2+X X^2  X  0 X^3+X X^3+X X^3+X^2 X^3+X^2+X X^2+X  X X^3 X^3+X^2+X X^3+X^2  X X^2+X  X X^3 X^3+X  X  X X^2  0  X X^3+X  X  0  X X^3+X  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+98x^94+202x^95+177x^96+204x^97+115x^98+106x^99+48x^100+16x^101+20x^102+16x^103+8x^104+5x^108+5x^110+1x^112+1x^114+1x^130

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 0.735 seconds.