The generator matrix

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

generates a code of length 98 over Z2[X]/(X^3) who´s minimum homogenous weight is 93.

Homogenous weight enumerator: w(x)=1x^0+280x^93+152x^94+354x^95+84x^96+286x^97+114x^98+224x^99+34x^100+132x^101+56x^102+98x^103+34x^104+62x^105+18x^106+28x^107+2x^108+20x^109+12x^110+32x^111+5x^112+16x^113+4x^117

The gray image is a linear code over GF(2) with n=392, k=11 and d=186.
This code was found by Heurico 1.16 in 22.9 seconds.