The generator matrix

 1  0  0  1  1  1  0  X  1  2  1  X X+2  X  1
 0  1  0  0  1  1  1  2  3 X+2 X+1  1  1  1  1
 0  0  1  1  X X+1  1  1  0  1  2 X+3  3 X+3  1
 0  0  0  2  0  2  2  0  2  2  2  0  2  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+76x^12+204x^13+118x^14+252x^15+119x^16+164x^17+56x^18+20x^19+12x^20+2x^22

The gray image is a code over GF(2) with n=60, k=10 and d=24.
This code was found by Heurico 1.11 in 0.00366 seconds.