The generator matrix

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

generates a code of length 31 over Z2[X]/(X^4) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+66x^27+326x^28+600x^29+784x^30+734x^31+677x^32+468x^33+264x^34+86x^35+52x^36+28x^37+6x^38+2x^39+2x^42

The gray image is a linear code over GF(2) with n=248, k=12 and d=108.
This code was found by Heurico 1.16 in 0.093 seconds.