The generator matrix

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

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+94x^12+64x^13+94x^14+1x^16+2x^18

The gray image is a code over GF(2) with n=104, k=8 and d=48.
This code was found by Heurico 1.16 in 6.87e-008 seconds.