The generator matrix

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

generates a code of length 13 over Z4[X]/(X^3+2,2X) 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 -1.01e-007 seconds.