The generator matrix

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

generates a code of length 15 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+670x^12+1360x^14+1455x^16+560x^18+50x^20

The gray image is a code over GF(2) with n=60, k=12 and d=24.
This code was found by Heurico 1.11 in 38.7 seconds.