The generator matrix

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

generates a code of length 18 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+172x^13+1223x^14+4592x^15+13403x^16+28432x^17+35228x^18+28720x^19+13500x^20+4444x^21+1116x^22+192x^23+40x^24+8x^25+1x^30

The gray image is a code over GF(2) with n=144, k=17 and d=52.
This code was found by Heurico 1.16 in 25.2 seconds.