The generator matrix

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

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+208x^9+1477x^10+5332x^11+15146x^12+21104x^13+15390x^14+5224x^15+1387x^16+256x^17+5x^18+4x^19+2x^20

The gray image is a code over GF(2) with n=104, k=16 and d=36.
This code was found by Heurico 1.16 in 4.19 seconds.