The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  1 X^3  1  1 X^2+X  1  1  X  1 X^3+X^2  1  1 X^2  1  1  1 X^3+X  1  1 X^2+X  1  1 X^3+X^2+X X^3  1  1  1  1 X^2  1  1  0  1  1 X^3+X^2 X^3+X  1  1  X  1  1  1  1  1  1 X^2+X X^3+X X^3 X^2  X  1  1  1  1  1  1  1  X  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  0 X^2+X  1  1  1  1  1  1 X^3+X^2  1
 0  1 X+1 X^3+X^2+X X^2+1  1 X^3+X^2+1  0  1 X^3+X^2+X X+1  1 X^3+X^2 X^2+X+1  1  X  1  1 X^3+X^2+X+1  1 X^3+X^2  X X^3+1  1 X^3 X^3+X+1  1 X^2+X X^3+1  1  1 X+1 X^3+X X^3+X^2 X^3+1  1 X^2+X+1 X^3+X^2+1  1  X X^3  1  1 X^3+X^2 X^3+X^2+1  1 X^2+X+1 X^3+X X^3+X^2+X  0 X+1  1  1  1  1  1 X^3  0 X^3+X X^3+X+1 X^2+1 X^3+X^2+X X^2+X+1 X^2  1 X^3+X^2+X X^2  X  0 X^2 X^3+X^2+X X^3 X^2  X  0 X^3+X  0 X^3+X X^2+1  X X^3+X^2 X^2  0  1  X  X X^2+1 X^2  1  X X^2+X+1 X+1 X^3+X^2+X+1 X^3+X^2+1 X^3+X^2  X  0
 0  0 X^2  0  0  0  0 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^3 X^3+X^2 X^3 X^3 X^2 X^2 X^3 X^3 X^3 X^3+X^2  0  0 X^3 X^3+X^2 X^2 X^3+X^2  0  0 X^3 X^2 X^2 X^2 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3 X^2 X^3 X^3+X^2  0 X^3 X^2 X^3 X^2 X^3 X^3+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+X^2  0  0 X^2  0 X^3+X^2 X^3 X^2 X^3  0 X^2 X^3+X^2 X^3  0 X^2 X^2  0 X^3  0  0  0 X^3+X^2  0 X^2 X^2  0  0 X^3+X^2 X^3 X^3+X^2 X^2 X^2 X^3+X^2  0 X^2  0
 0  0  0 X^3+X^2 X^3 X^3+X^2 X^2 X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^2  0 X^3+X^2 X^3  0 X^2 X^3+X^2 X^3  0 X^3+X^2 X^3 X^3+X^2 X^2 X^3+X^2  0 X^3+X^2 X^2 X^3 X^3+X^2 X^3  0  0 X^3 X^2  0  0 X^3+X^2 X^3 X^3 X^2  0 X^3+X^2 X^3+X^2 X^3 X^2 X^2  0  0  0  0  0  0 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^3 X^3+X^2 X^2 X^3+X^2 X^3 X^2 X^2 X^2 X^3 X^2 X^2 X^3 X^3 X^3 X^3 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^2  0 X^3+X^2 X^3+X^2 X^3 X^2  0 X^3 X^3+X^2 X^3 X^2 X^2  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+226x^92+280x^93+514x^94+488x^95+403x^96+460x^97+400x^98+376x^99+406x^100+284x^101+152x^102+28x^103+34x^104+22x^106+4x^107+2x^108+4x^110+4x^112+2x^118+2x^122+2x^124+1x^132+1x^140

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 1.17 seconds.