The generator matrix

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

generates a code of length 17 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+66x^13+196x^14+388x^15+829x^16+1150x^17+856x^18+376x^19+128x^20+62x^21+36x^22+4x^23+2x^24+2x^25

The gray image is a code over GF(2) with n=136, k=12 and d=52.
This code was found by Heurico 1.16 in 14.4 seconds.