The generator matrix

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

generates a code of length 17 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+85x^8+48x^10+380x^12+744x^14+2915x^16+2600x^18+1032x^20+184x^22+167x^24+8x^26+28x^28

The gray image is a code over GF(2) with n=68, k=13 and d=16.
This code was found by Heurico 1.16 in 0.19 seconds.