The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  2  X  1  1
 0  X  0  X  0  2  X X+2  0  X  2  2  0  X X+2  0  2
 0  0  X  X  0  X X+2  2  2  X X+2  2  X X+2  0  2  2
 0  0  0  2  2  2  0  2  2  0  0  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 14.

Homogenous weight enumerator: w(x)=1x^0+18x^14+36x^15+50x^16+64x^17+40x^18+20x^19+12x^20+8x^21+5x^22+1x^24+1x^30

The gray image is a code over GF(2) with n=68, k=8 and d=28.
This code was found by Heurico 1.16 in 0.00282 seconds.