The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+177x^8+938x^9+3371x^10+11338x^11+27663x^12+44020x^13+27739x^14+11428x^15+3322x^16+866x^17+185x^18+18x^19+5x^20+1x^22

The gray image is a code over GF(2) with n=104, k=17 and d=32.
This code was found by Heurico 1.16 in 12.9 seconds.