The generator matrix

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

generates a code of length 16 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+114x^14+156x^15+65x^16+72x^17+30x^18+28x^19+46x^20

The gray image is a code over GF(2) with n=64, k=9 and d=28.
This code was found by Heurico 1.16 in 0.284 seconds.