The generator matrix

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

generates a code of length 13 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+163x^10+864x^11+1476x^12+3218x^13+1458x^14+830x^15+155x^16+14x^17+11x^18+2x^19

The gray image is a code over GF(2) with n=104, k=13 and d=40.
This code was found by Heurico 1.16 in 0.078 seconds.