The generator matrix

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

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+104x^10+146x^11+308x^12+422x^13+1116x^14+858x^15+4593x^16+1214x^17+4636x^18+918x^19+1152x^20+402x^21+276x^22+126x^23+86x^24+10x^25+12x^26+4x^28

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 1.47 seconds.