The generator matrix

 1  1  1  1  1  1  1  1  X  1  2  X  X  1  X  1
 0  X  0  0  0  0  0  0 X+2  X  X  2  2  2  2  X
 0  0  X  0  0  0  X X+2  X  X  2  X  2  0  2  X
 0  0  0  X  0  X  X  X  2  2  2  2  X  0 X+2  0
 0  0  0  0  X  X  2 X+2 X+2  2 X+2  0 X+2  0  2  0
 0  0  0  0  0  2  2  2  2  0  2  0  0  2  2  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+43x^10+74x^11+141x^12+280x^13+469x^14+598x^15+730x^16+820x^17+487x^18+214x^19+143x^20+48x^21+23x^22+10x^23+9x^24+4x^25+2x^26

The gray image is a code over GF(2) with n=64, k=12 and d=20.
This code was found by Heurico 1.16 in 0.12 seconds.