The generator matrix

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

generates a code of length 17 over Z2[X]/(X^4) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+124x^14+466x^15+811x^16+1430x^17+692x^18+350x^19+156x^20+58x^21+8x^22

The gray image is a linear code over GF(2) with n=136, k=12 and d=56.
This code was found by Heurico 1.16 in 0.093 seconds.