The generator matrix

 1  0  1  1  1 X^3 X^2+X  1  1 X^3+X^2+X  1  1  1  1  1 X^2  1  1  X  1  1  X X^2  1  X  0  1  X  1  1  1
 0  1 X+1 X^3+X^2+X X^2+1  1  1 X^3 X^2+X  1 X^3+1 X^2+X+1 X^3+X^2+1 X+1 X^2  1  X X^2  1 X^3+X  1  0  1 X^2+X X^3+X^2+X  X X^3+X^2+X+1  1 X^3 X^2 X^3+X
 0  0 X^2 X^3+X^2 X^3 X^2  0 X^2  0 X^3+X^2 X^3 X^3+X^2 X^2  0 X^2 X^2 X^3+X^2 X^3 X^3 X^3 X^3+X^2 X^3+X^2 X^3 X^2 X^3+X^2 X^2 X^3 X^2 X^3+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 29.

Homogenous weight enumerator: w(x)=1x^0+198x^29+318x^30+168x^31+125x^32+108x^33+64x^34+24x^35+14x^37+2x^38+2x^40

The gray image is a linear code over GF(2) with n=248, k=10 and d=116.
This code was found by Heurico 1.16 in 48.5 seconds.