The generator matrix

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

generates a code of length 16 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+122x^10+420x^11+1084x^12+2398x^13+3548x^14+5792x^15+5791x^16+6054x^17+3698x^18+2372x^19+976x^20+346x^21+120x^22+24x^23+20x^24+2x^25

The gray image is a code over GF(2) with n=64, k=15 and d=20.
This code was found by Heurico 1.13 in 1.87 seconds.