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

generates a code of length 98 over Z2[X]/(X^4) who´s minimum homogenous weight is 93.

Homogenous weight enumerator: w(x)=1x^0+244x^93+863x^94+864x^95+1339x^96+876x^97+918x^98+704x^99+673x^100+368x^101+438x^102+272x^103+264x^104+128x^105+131x^106+40x^107+40x^108+24x^109+1x^110+1x^116+2x^120+1x^122

The gray image is a linear code over GF(2) with n=784, k=13 and d=372.
This code was found by Heurico 1.16 in 4.22 seconds.