The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1 X^3  1  X  1 X^3  X  1  X  0
 0  X  0  X X^3  0 X^3+X  X X^2 X^2+X X^2 X^3+X^2+X X^3+X^2 X^2 X^2+X X^2+X  X X^2 X^3+X X^3  X X^3+X^2+X X^3+X^2 X^3+X X^3+X^2  X X^2  X X^2+X X^3+X^2+X  X
 0  0  X  X X^2 X^2+X X^2+X X^2 X^2 X^3  X X^3+X  0 X^2+X X^3+X^2+X X^3+X^2  X X^3+X  X  X X^3+X^2+X X^2+X  X X^3 X^2+X X^3+X^2+X X^2 X^3+X^2  0 X^3+X^2+X X^3
 0  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0  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+312x^28+128x^29+510x^30+256x^31+438x^32+128x^33+188x^34+76x^36+6x^38+4x^40+1x^48

The gray image is a linear code over GF(2) with n=248, k=11 and d=112.
This code was found by Heurico 1.16 in 1.22 seconds.