The generator matrix

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

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+121x^28+248x^30+256x^31+338x^32+8x^34+51x^36+1x^56

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 0.141 seconds.