The generator matrix

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

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+148x^10+490x^12+128x^13+1258x^14+896x^15+2331x^16+896x^17+1298x^18+128x^19+486x^20+110x^22+20x^24+2x^26

The gray image is a code over GF(2) with n=64, k=13 and d=20.
This code was found by Heurico 1.16 in 1.71 seconds.