The generator matrix

 1  0  0  1  1  1  2  2  1  X  1  1  1  1  1  X  0
 0  1  0  0  3  3  1  1 X+2  1 X+3 X+2  2 X+2  X  1 X+2
 0  0  1 X+1 X+3  2  1  X  0  X  3  X  1 X+3 X+2  0  1
 0  0  0  2  2  0  2  0  2  2  0  2  0  0  0  0  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+95x^14+176x^15+177x^16+176x^17+154x^18+144x^19+52x^20+16x^21+31x^22+2x^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 0.00923 seconds.