The generator matrix

 1  0  1  1  1  X  1  1  1  1  2 X+2  0  0  1  1
 0  1  1  2 X+1  1  X X+3 X+2  3  X  1  0  1  0 X+2
 0  0  X X+2  2 X+2  X X+2  2  0 X+2 X+2  X  2  2  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+66x^14+48x^15+79x^16+24x^18+16x^19+16x^20+6x^22

The gray image is a code over GF(2) with n=64, k=8 and d=28.
This code was found by Heurico 1.16 in 0.00157 seconds.