The generator matrix

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

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+190x^11+148x^12+404x^13+80x^14+160x^15+27x^16+12x^17+2x^19

The gray image is a code over GF(2) with n=104, k=10 and d=44.
This code was found by Heurico 1.16 in 1.05e-007 seconds.