The generator matrix

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

generates a code of length 17 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+51x^10+88x^11+223x^12+456x^13+843x^14+1894x^15+2972x^16+3272x^17+2989x^18+1982x^19+853x^20+424x^21+201x^22+66x^23+47x^24+8x^25+12x^26+2x^27

The gray image is a code over GF(2) with n=68, k=14 and d=20.
This code was found by Heurico 1.16 in 1.44 seconds.