The generator matrix

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

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+42x^13+202x^14+444x^15+685x^16+1358x^17+729x^18+400x^19+152x^20+54x^21+20x^22+4x^23+2x^24+2x^25+1x^26

The gray image is a linear code over GF(2) with n=136, k=12 and d=52.
This code was found by Heurico 1.16 in 0.063 seconds.