The generator matrix

 1  0  1  1  1  2 X^2+X  1  1 X^2+X+2  1  X  1  1  1  1
 0  1 X+1 X^2+X+2 X^2+1  1  1  2 X^2+X  1  3  X X^2+X+1 X^2+1  1 X+1
 0  0 X^2 X^2+2  2 X^2  0 X^2  0 X^2+2  2 X^2+2 X^2+2 X^2+2 X^2 X^2+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+118x^14+288x^15+283x^16+192x^17+100x^18+32x^19+4x^20+6x^22

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 1.05e-007 seconds.