The generator matrix

 1  0  1  1  1 X+2  1  2  1  1  2  1  X  2  2  1
 0  1  1 X+2 X+3  1  2  1 X+1  X  1 X+1  2  X  X  0
 0  0  X  0 X+2  2  X  X  0 X+2 X+2  2  X X+2  2  0
 0  0  0  2  0  2  0  2  0  2  0  0  2  2  0  0
 0  0  0  0  2  0  2  0  2  0  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 12.

Homogenous weight enumerator: w(x)=1x^0+42x^12+122x^13+60x^14+282x^15+55x^16+244x^17+56x^18+100x^19+30x^20+18x^21+12x^22+2x^23

The gray image is a code over GF(2) with n=64, k=10 and d=24.
This code was found by Heurico 1.16 in 0.00897 seconds.