The generator matrix

 1  0  0  1  1  1 X+2  1  1  1  1  0  0  1  1
 0  1  0  1  0 X+3  1  1  2  X  1  1 X+2  X  0
 0  0  1  1  1  0  1  1  0  3  2 X+1  1 X+1 X+2
 0  0  0  X  0  0  0  2  X  X  2  X  0 X+2  2
 0  0  0  0  X X+2 X+2  0  2  X X+2 X+2  X  0  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+78x^10+190x^11+531x^12+964x^13+1454x^14+1780x^15+1409x^16+992x^17+543x^18+158x^19+75x^20+12x^21+4x^22+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 0.357 seconds.