The generator matrix

 1  0  0  0  1  1  1 X^2+X  1 X^3+X X^2+X  1  0  1
 0  1  0  0  X X^3+1 X^2+X+1  1 X^3 X^2  1 X^2  X X^2+X
 0  0  1  0 X+1  1  X X+1 X^2+X+1 X^2+X X^3+X^2+1  0  1 X^3+X^2+1
 0  0  0  1  1 X^2 X+1 X+1 X^2  1 X^3+X  1 X^2+1  X
 0  0  0  0 X^2 X^3  0  0 X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2 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+142x^9+1281x^10+6046x^11+23033x^12+58786x^13+83372x^14+58996x^15+23245x^16+5882x^17+1137x^18+190x^19+25x^20+6x^21+2x^22

The gray image is a linear code over GF(2) with n=112, k=18 and d=36.
This code was found by Heurico 1.16 in 57.5 seconds.