The generator matrix

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

generates a code of length 13 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+168x^8+1144x^9+5577x^10+20056x^11+59904x^12+88528x^13+59599x^14+20368x^15+5619x^16+952x^17+199x^18+24x^19+4x^20+1x^22

The gray image is a code over GF(2) with n=104, k=18 and d=32.
This code was found by Heurico 1.16 in 52.9 seconds.