The generator matrix

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

generates a code of length 17 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+182x^14+319x^16+388x^18+92x^20+38x^22+4x^24

The gray image is a code over GF(2) with n=68, k=10 and d=28.
This code was found by Heurico 1.16 in 26.1 seconds.