The generator matrix

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

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+83x^14+91x^16+76x^18+4x^20+1x^30

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 0.00164 seconds.