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

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+150x^92+480x^93+387x^94+442x^95+468x^96+430x^97+416x^98+392x^99+321x^100+316x^101+133x^102+90x^103+31x^104+22x^105+6x^106+4x^107+1x^108+4x^116+1x^130+1x^138

The gray image is a linear code over GF(2) with n=776, k=12 and d=368.
This code was found by Heurico 1.16 in 1.45 seconds.