The generator matrix

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

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+188x^93+435x^94+388x^95+383x^96+458x^97+622x^98+368x^99+346x^100+308x^101+279x^102+140x^103+87x^104+62x^105+6x^106+12x^108+4x^109+3x^112+1x^114+4x^121+1x^146

The gray image is a linear code over GF(2) with n=784, k=12 and d=372.
This code was found by Heurico 1.16 in 1.52 seconds.