The generator matrix

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

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+540x^13+2196x^14+6638x^15+14371x^16+17922x^17+14626x^18+6604x^19+2044x^20+544x^21+40x^22+6x^23+2x^25+2x^26

The gray image is a linear code over GF(2) with n=136, k=16 and d=52.
This code was found by Heurico 1.16 in 6.44 seconds.