The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+216x^9+1453x^10+5502x^11+14608x^12+21792x^13+15006x^14+5356x^15+1303x^16+280x^17+13x^18+6x^19

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 4.5 seconds.