The generator matrix

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

generates a code of length 14 over Z2[X]/(X^4) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+48x^9+704x^10+3112x^11+11394x^12+28628x^13+43077x^14+28944x^15+11508x^16+2904x^17+634x^18+104x^19+8x^20+4x^21+1x^22+1x^24

The gray image is a linear code over GF(2) with n=112, k=17 and d=36.
This code was found by Heurico 1.16 in 14.8 seconds.