The generator matrix

 1  0  0  0  1  1  1  X  1  1 X+2  2  0 X+2  1  1
 0  1  0  0  0  1 X+3  1 X+2 X+3  1  1  1  X  2  0
 0  0  1  0  1 X+1  X  1  0 X+1  0  3  1  1  2  0
 0  0  0  1  1  X X+1 X+1 X+1  1 X+1 X+3 X+2 X+2 X+2  0
 0  0  0  0  2  0  0  0  2  2  2  0  2  2  0  0
 0  0  0  0  0  2  0  0  2  2  0  2  2  0  0  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+83x^10+144x^11+611x^12+1064x^13+2003x^14+2640x^15+3289x^16+2624x^17+2051x^18+1056x^19+576x^20+152x^21+85x^22+2x^24+2x^26+1x^28

The gray image is a code over GF(2) with n=64, k=14 and d=20.
This code was found by Heurico 1.16 in 1.08 seconds.