The generator matrix

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

generates a code of length 98 over Z2[X]/(X^4) who´s minimum homogenous weight is 92.

Homogenous weight enumerator: w(x)=1x^0+288x^92+822x^93+1348x^94+1850x^95+1842x^96+1810x^97+1795x^98+1714x^99+1191x^100+1132x^101+934x^102+520x^103+423x^104+298x^105+140x^106+142x^107+70x^108+16x^109+22x^110+14x^111+5x^112+1x^114+3x^116+2x^117+1x^120

The gray image is a linear code over GF(2) with n=784, k=14 and d=368.
This code was found by Heurico 1.16 in 12.8 seconds.