The generator matrix

 1  0  0  1  1  1  X  1  1  2  1 X+2  2  1  1  1
 0  1  0  1 X+2 X+3  1  0  3  1  X  1  1  3 X+1  X
 0  0  1  1 X+3 X+2  1 X+2 X+1  X  1 X+1  1 X+1  0  1
 0  0  0  2  0  0  0  0  0  0  2  2  2  2  2  0
 0  0  0  0  2  0  0  0  0  2  2  0  2  2  0  2
 0  0  0  0  0  2  0  0  2  2  0  0  2  2  0  0
 0  0  0  0  0  0  2  0  2  0  0  2  0  2  0  2
 0  0  0  0  0  0  0  2  2  2  0  2  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+72x^10+80x^11+544x^12+1040x^13+1712x^14+2976x^15+3529x^16+2976x^17+1736x^18+1040x^19+520x^20+80x^21+64x^22+14x^24

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 12.6 seconds.