The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+124x^11+201x^12+404x^13+168x^14+100x^15+13x^16+12x^17+1x^20

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.