The generator matrix

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

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+114x^12+378x^13+448x^14+784x^15+681x^16+772x^17+424x^18+352x^19+114x^20+18x^21+8x^22+2x^24

The gray image is a code over GF(2) with n=64, k=12 and d=24.
This code was found by Heurico 1.16 in 0.0932 seconds.