The generator matrix

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

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+370x^12+592x^14+823x^16+208x^18+54x^20

The gray image is a code over GF(2) with n=60, k=11 and d=24.
This code was found by Heurico 1.11 in 11.3 seconds.