The generator matrix

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

generates a code of length 13 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+318x^11+276x^12+916x^13+208x^14+288x^15+27x^16+12x^17+2x^19

The gray image is a code over GF(2) with n=104, k=11 and d=44.
This code was found by Heurico 1.16 in 3.25 seconds.