The generator matrix

 1  0  0  1  1  1  0 X^3  1  1 X^3 X^2  1  1  1  1  1  1 X^3+X^2+X X^3+X  X X^3+X^2+X X^3+X X^3+X  1  1  1  1  1 X^3+X^2+X X^3+X  1 X^3  0  1  1 X^2+X  1  1 X^3+X^2  1  X  1 X^3+X X^3+X^2+X  1  1  1 X^3+X^2 X^3+X^2 X^2  1  1 X^3  1 X^2+X  1  1  1  1  X  1 X^3+X  0  1  1 X^2  1  1  1  1  1  1 X^2  X  0 X^2+X  1  1 X^3+X^2+X  1 X^2  1  1 X^2+X  0  1 X^3+X^2 X^3+X^2  1  1  1  1  1  1  1  1
 0  1  0  0 X^2+1 X^2+1  1 X^3+X^2+X X^3 X^3+X^2+1  1  1 X^3+X^2 X^3+X^2+1 X^2+X+1 X^3+X^2+X X^2+X X^3+X^2+X+1 X^2  1  1  1  1 X^3+X^2+X X+1 X^3+X X^2+X  1 X^3+1  1  X X^2+X+1  1 X^3+X X^2+X+1  X  1 X^3+X+1 X^2  1 X^3+X^2+X  1 X^3 X^3  1 X^2+X X^2+1  1  1 X^3+X  1 X^3+X^2 X^2+X  1 X^3+1  0 X^2 X^3+X^2+X X^3+X+1 X^3+1  1 X^2+1  1 X^2 X^2 X^3+X^2+X+1  1  0 X^3+1 X^3 X^3+X^2+X+1 X^3+X^2+X+1 X^3+X^2 X^3  1  1  0  X X^3 X^3+X X^3+X  1 X^3+X^2+1 X^2+X  1 X^3 X^3+X+1  1 X^3+X^2+X  X X^3+X+1 X^3+X^2 X^2+1 X^3+X^2+1 X^3+X  X  0
 0  0  1 X+1 X^3+X+1 X^3 X^3+X^2+X+1  1 X^3+X^2+X X^2+1  1 X^3+X X^3+X^2+1 X^3+X X^3  X  1 X^3+1  1 X+1 X^2  1 X^3+X^2+X  1 X^3+X+1 X^3+X^2 X+1  0 X^2+X+1 X^2+X  1 X^2+X X^2+1  1 X^2+1 X+1 X+1 X^2 X^3+X+1 X^3+X+1 X^3+X^2+X  0 X^3  1 X^2+1 X^2 X^2+X X^3+1 X^2+X  1 X^3 X^2  X X^3+X^2+1 X^3+X  1 X^3+X^2+X X^3+X^2+1 X^3+X X^3+X^2+1 X^3+X^2+X+1 X^3+X^2 X^2+1  1  X X^2+X X^3 X^3+1 X^3+X X^3+X^2+X+1 X^3+X+1 X^3 X^2  1 X^3 X^2+X  1 X^2+X+1  1  1 X^3+1 X+1 X+1 X^3+X^2 X^3+X+1  1 X^3+X+1 X^2+X  1  X X^3+X^2+X  0 X^3+X^2+X+1 X^2+1 X^3+X^2+1 X^3+X X^2+X
 0  0  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3  0 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 X^3  0 X^3  0  0  0  0  0 X^3 X^3  0  0  0  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3  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+303x^92+720x^93+1022x^94+1076x^95+1036x^96+892x^97+880x^98+558x^99+440x^100+388x^101+306x^102+208x^103+145x^104+84x^105+36x^106+30x^107+43x^108+12x^109+9x^110+2x^114+1x^118

The gray image is a linear code over GF(2) with n=776, k=13 and d=368.
This code was found by Heurico 1.16 in 7.48 seconds.