The generator matrix

 1  0  0  0  1  1  1  2  1  1  1  1  1  1  1  1
 0  1  0  0  1  2  3  1  0  X X+1  3  X X+1  0  1
 0  0  1  0  1  3  2  3  X  1 X+1  0  2  3 X+2 X+1
 0  0  0  1  2  1  3  3 X+1  X  1 X+2  2 X+2  2 X+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+144x^12+276x^13+590x^14+632x^15+861x^16+608x^17+540x^18+264x^19+160x^20+12x^21+6x^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 1.11 in 0.811 seconds.