The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X  0  X  2 X+2  0  X X^2 X^2+X X^2+2 X^2+X+2 X^2 X^2 X^2+X+2 X^2+X+2
 0  0  X  X X^2 X^2+X X^2+X X^2  X X^2+X+2 X^2+2 X+2 X^2+X  2  0 X^2

generates a code of length 16 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+192x^14+638x^16+192x^18+1x^32

The gray image is a code over GF(2) with n=128, k=10 and d=56.
This code was found by Heurico 1.16 in 0.187 seconds.