The generator matrix

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

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+260x^13+1154x^14+3266x^15+6923x^16+9392x^17+7292x^18+3158x^19+980x^20+300x^21+34x^22+6x^23+2x^27

The gray image is a linear code over GF(2) with n=136, k=15 and d=52.
This code was found by Heurico 1.16 in 2.31 seconds.