The generator matrix

 1  0  0  0  1  1  1 X+2  1  1 X+2  1  X  1  1
 0  1  0  0  0  3  1  1  X X+1  1 X+3  X X+1  0
 0  0  1  0  1  1  X X+1  3  2  3 X+3  1  0  0
 0  0  0  1  1  X X+1 X+1  2  0 X+2  3 X+1 X+2  0
 0  0  0  0  2  0  2  0  0  2  2  2  2  2  2

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+51x^10+262x^11+486x^12+946x^13+1495x^14+1676x^15+1543x^16+980x^17+465x^18+206x^19+50x^20+26x^21+5x^22

The gray image is a code over GF(2) with n=60, k=13 and d=20.
This code was found by Heurico 1.13 in 0.418 seconds.