The generator matrix

 1  0  0  0  0  1  1  1  X  1  1  1  1  X  X  1
 0  1  0  0  0  0  2  2  0  3 X+1 X+2  3  1  1  X
 0  0  1  0  0  0  3 X+1  1  2  X  3 X+3 X+2  X X+2
 0  0  0  1  0  1 X+1  X  1  3  X  0  3  3 X+3  2
 0  0  0  0  1  1  X X+1 X+1  X  0  X X+1 X+3  0  2
 0  0  0  0  0  2  0  0  2  0  2  2  2  0  0  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+145x^10+686x^11+1873x^12+3956x^13+7838x^14+11682x^15+13072x^16+11768x^17+7858x^18+4114x^19+1783x^20+532x^21+190x^22+30x^23+7x^24+1x^26

The gray image is a code over GF(2) with n=64, k=16 and d=20.
This code was found by Heurico 1.13 in 5.92 seconds.