The generator matrix

 1  0  0  1  1  1 X+2  1  1  1 X+2  1  1  1  0
 0  1  0  0  1 X+1  1  2 X+3  2  0 X+2 X+2 X+2  1
 0  0  1 X+1 X+3  0 X+1  X  1  1  1  0 X+2  2 X+1
 0  0  0  2  0  0  0  0  2  0  2  2  0  2  2
 0  0  0  0  2  2  0  0  2  2  2  2  0  0  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+236x^12+256x^13+400x^14+256x^15+437x^16+256x^17+176x^18+28x^20+2x^24

The gray image is a code over GF(2) with n=60, k=11 and d=24.
This code was found by Heurico 1.16 in 5.11 seconds.