The generator matrix

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

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+24x^29+270x^30+48x^31+77x^32+24x^33+66x^34+2x^44

The gray image is a linear code over GF(2) with n=248, k=9 and d=116.
This code was found by Heurico 1.16 in 0.016 seconds.