The generator matrix

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

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+208x^27+294x^28+482x^29+610x^30+946x^31+666x^32+502x^33+146x^34+108x^35+60x^36+54x^37+11x^38+2x^39+3x^40+2x^41+1x^46

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 54 seconds.