The generator matrix

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

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+66x^28+176x^29+192x^30+176x^31+183x^32+152x^33+62x^34+6x^36+8x^37+2x^42

The gray image is a linear code over GF(2) with n=248, k=10 and d=112.
This code was found by Heurico 1.16 in 0.015 seconds.