The generator matrix

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

generates a code of length 31 over Z2[X]/(X^4) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+142x^28+376x^29+339x^30+448x^31+264x^32+288x^33+126x^34+32x^35+8x^36+8x^37+15x^38+1x^40

The gray image is a linear code over GF(2) with n=248, k=11 and d=112.
This code was found by Heurico 1.16 in 0.219 seconds.