The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X
 0 X^3  0  0  0  0  0  0  0  0 X^3 X^3  0  0 X^3 X^3 X^3
 0  0 X^3  0  0  0  0  0  0 X^3 X^3 X^3  0 X^3 X^3  0  0
 0  0  0 X^3  0  0  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0
 0  0  0  0 X^3  0  0  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3
 0  0  0  0  0 X^3  0  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0
 0  0  0  0  0  0 X^3  0 X^3 X^3 X^3  0  0  0  0 X^3 X^3
 0  0  0  0  0  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0

generates a code of length 17 over Z2[X]/(X^4) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+76x^12+40x^14+165x^16+1536x^17+80x^18+108x^20+8x^22+34x^24

The gray image is a linear code over GF(2) with n=136, k=11 and d=48.
This code was found by Heurico 1.16 in 0.062 seconds.