The generator matrix

 1  1  1  1  1  1  1  X  1  1  X  X  2  X 2X  0  2
 0 2X  0 2X  0 2X  0 2X 2X  0 2X  0 2X  0 2X 2X  0

generates a code of length 17 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+22x^17+2x^18+6x^19+1x^20

The gray image is a code over GF(2) with n=136, k=5 and d=68.
This code was found by Heurico 1.16 in 1.05e-007 seconds.