The generator matrix

 1  0  0  0  1  1  1  0  1  2  1  1  1  X  0
 0  1  0  0  0  1  3  1  X  X X+1  3  3  1  1
 0  0  1  0  1  1  0 X+1 X+1  1  X  1 X+2  1  1
 0  0  0  1  1  0 X+1 X+1  X X+1 X+2  1 X+3 X+3  3
 0  0  0  0  2  0  2  0  0  0  2  0  2  0  2
 0  0  0  0  0  2  2  2  0  2  2  0  0  0  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+147x^10+446x^11+1050x^12+1774x^13+3151x^14+3228x^15+3135x^16+1836x^17+1105x^18+358x^19+102x^20+38x^21+13x^22

The gray image is a code over GF(2) with n=60, k=14 and d=20.
This code was found by Heurico 1.16 in 1.05 seconds.