The generator matrix

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

generates a code of length 16 over Z4[X]/(X^2+2X+2) 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 0.016 seconds.