The generator matrix

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

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+201x^10+88x^11+680x^12+760x^13+2344x^14+2224x^15+3745x^16+2224x^17+2426x^18+760x^19+672x^20+88x^21+144x^22+22x^24+5x^26

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 8.25 seconds.