The generator matrix

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

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+268x^13+1204x^14+3034x^15+7205x^16+9274x^17+7360x^18+3036x^19+1080x^20+248x^21+44x^22+10x^23+2x^24+2x^25

The gray image is a code over GF(2) with n=136, k=15 and d=52.
This code was found by Heurico 1.16 in 1.94 seconds.