The generator matrix

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

generates a code of length 15 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+113x^8+120x^10+1024x^12+2712x^14+3147x^16+744x^18+288x^20+8x^22+35x^24

The gray image is a code over GF(2) with n=60, k=13 and d=16.
This code was found by Heurico 1.16 in 0.181 seconds.