The generator matrix

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

generates a code of length 13 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+19x^12+20x^13+19x^14+4x^15+1x^18

The gray image is a code over GF(2) with n=104, k=6 and d=48.
This code was found by Heurico 1.16 in -3.24e-008 seconds.