The generator matrix

 1  0  0  0  1  1  1  1  2  X  1  0  1  1 X+2  0
 0  1  0  0  0  1  2 X+3  1  1 X+2  1 X+1  X  1  0
 0  0  1  0  0  1  3  2 X+1  3  3  X X+3  0 X+2  1
 0  0  0  1 X+1  2  1  3  3  0 X+2  1  1  3 X+1 X+3
 0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  2

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+344x^12+512x^13+1248x^14+1024x^15+1934x^16+1024x^17+1248x^18+512x^19+344x^20+1x^32

The gray image is a code over GF(2) with n=64, k=13 and d=24.
This code was found by Heurico 1.16 in 15.1 seconds.