The generator matrix

 1  0  0  1  1  1  X  1  1  1  1  1  1  1  1  1
 0  1  0  1  0 X+3  1  0  X X+2  0 X+3 X+3 X+1 X+3  1
 0  0  1  1  1  0  1  0  1 X+1  X X+1 X+3 X+3  1  1
 0  0  0  X  0 X+2  2  X  0  X  2 X+2 X+2  0  0  0
 0  0  0  0  X  0  2 X+2  0  X X+2  2 X+2  X  2  0
 0  0  0  0  0  2  2  0  2  2  2  2  0  2  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+75x^10+170x^11+441x^12+856x^13+2238x^14+1994x^15+4709x^16+2144x^17+2292x^18+830x^19+406x^20+136x^21+66x^22+14x^23+10x^24+1x^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 1.18 seconds.