The generator matrix

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

generates a code of length 13 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+104x^9+759x^10+2700x^11+7104x^12+11432x^13+7138x^14+2672x^15+727x^16+112x^17+15x^18+4x^19

The gray image is a code over GF(2) with n=104, k=15 and d=36.
This code was found by Heurico 1.16 in 1.16 seconds.