The generator matrix

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

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 1.16 in 9.22 seconds.