The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  1  0  1  1
 0  X  0  X  0  2  X X+2  0  X X+2  2  X X+2  X
 0  0  X  X  0  X X+2  2  2  X  0  2  2  X  X
 0  0  0  2  2  2  0  2  2  0  2  2  0  2  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+20x^12+26x^13+77x^14+16x^15+75x^16+20x^17+15x^18+2x^21+3x^22+1x^26

The gray image is a code over GF(2) with n=60, k=8 and d=24.
This code was found by Heurico 1.16 in 0.00187 seconds.