The generator matrix

 1  0  0  1  1  1  0  2  1  X  1  1  1  1  1 X+2  2
 0  1  0  0  1  1  1  1  X  1 X+1 X+2  X  3  2  1  1
 0  0  1  1  2  3 X+1  X  0  X X+3  X X+1 X+1  0 X+2 X+1
 0  0  0  2  0  2  2  0  2  2  0  2  0  2  2  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+106x^14+156x^15+157x^16+220x^17+161x^18+116x^19+56x^20+20x^21+28x^22+2x^24+1x^26

The gray image is a code over GF(2) with n=68, k=10 and d=28.
This code was found by Heurico 1.11 in 0.00473 seconds.