The generator matrix

 1  0  0  0  1  1  1  1  2  1  1  1  1  1  1  1
 0  1  0  0  0  1  2  3  1 X+2  3 X+1 X+1  1  0 X+2
 0  0  1  0  0  1  3  2  3  1  0  1 X+1 X+2 X+2 X+1
 0  0  0  1 X+1  2  1  3  3  X  0 X+2  3  3 X+1  2
 0  0  0  0  2  0  0  0  0  0  2  2  2  2  2  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+432x^12+384x^13+1128x^14+1200x^15+1937x^16+1072x^17+1280x^18+400x^19+312x^20+16x^21+24x^22+6x^24

The gray image is a code over GF(2) with n=64, k=13 and d=24.
This code was found by Heurico 1.13 in 475 seconds.