The generator matrix

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

generates a code of length 31 over Z2[X]/(X^4) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+44x^24+16x^26+124x^28+320x^30+1024x^31+381x^32+48x^34+64x^36+20x^40+4x^44+2x^48

The gray image is a linear code over GF(2) with n=248, k=11 and d=96.
This code was found by Heurico 1.16 in 0.062 seconds.