The generator matrix

 1  1  1  1  X  X  X  1  1  0  1  1  X  X  1
 0  X  0  X  0  X  X  0  0  2  X X+2  X X+2  0
 0  0  X  X  X  X  0  0 X+2  X  X  0 X+2  0  0
 0  0  0  2  0  0  0  0  0  0  0  2  2  2  0
 0  0  0  0  2  0  0  0  0  2  2  2  2  2  0
 0  0  0  0  0  2  0  0  0  0  2  2  0  2  0
 0  0  0  0  0  0  2  0  0  0  2  2  2  0  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  0  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+71x^8+214x^10+384x^11+704x^12+2072x^14+1280x^15+2087x^16+724x^18+384x^19+208x^20+56x^22+1x^24+6x^26

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 0.196 seconds.