The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+38x^12+48x^13+38x^14+1x^16+2x^18

The gray image is a code over GF(2) with n=104, k=7 and d=48.
This code was found by Heurico 1.16 in -3.24e-008 seconds.