The generator matrix

 1  0  0  1  1  1  2  1  1  X  1  2  1  0  1
 0  1  0  1  X X+3  1  0  2  1  1  1  1  X X+3
 0  0  1  1  1  0 X+1  X X+1  1  X  0 X+1  1  0
 0  0  0  X  0 X+2  X X+2 X+2  0  2 X+2  X  X  X
 0  0  0  0  2  0  2  0  2  2  2  0  0  2  2
 0  0  0  0  0  2  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 10.

Homogenous weight enumerator: w(x)=1x^0+80x^10+204x^11+509x^12+964x^13+1439x^14+1768x^15+1490x^16+952x^17+515x^18+204x^19+47x^20+4x^21+13x^22+1x^24+1x^26

The gray image is a code over GF(2) with n=60, k=13 and d=20.
This code was found by Heurico 1.16 in 0.316 seconds.