The generator matrix

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

generates a code of length 17 over Z2[X]/(X^4) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+116x^13+650x^14+1388x^15+3699x^16+4696x^17+3732x^18+1352x^19+588x^20+116x^21+34x^22+12x^23

The gray image is a linear code over GF(2) with n=136, k=14 and d=52.
This code was found by Heurico 1.16 in 0.562 seconds.