The generator matrix

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

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+112x^13+758x^14+1444x^15+3663x^16+4368x^17+3854x^18+1336x^19+668x^20+160x^21+10x^22+4x^23+4x^24+2x^26

The gray image is a code over GF(2) with n=136, k=14 and d=52.
This code was found by Heurico 1.16 in 0.5 seconds.