The generator matrix
1 1 1 1 1 1 1 1 X X 1 X 2 1 1 1 1
0 X 0 0 0 X X+2 X 2 0 0 X+2 X 0 X X 0
0 0 X 0 X X X+2 0 0 X 0 X 0 X+2 X+2 2 0
0 0 0 X X 0 X+2 X X X 2 X X 2 2 2 0
0 0 0 0 2 0 0 0 0 2 2 2 2 0 2 2 0
0 0 0 0 0 2 0 0 2 2 2 0 0 2 2 0 0
0 0 0 0 0 0 2 0 2 0 2 2 2 2 2 0 0
0 0 0 0 0 0 0 2 2 2 2 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 10.
Homogenous weight enumerator: w(x)=1x^0+44x^10+60x^11+173x^12+212x^13+592x^14+428x^15+2249x^16+612x^17+2280x^18+500x^19+610x^20+188x^21+144x^22+36x^23+38x^24+12x^25+12x^26+1x^28
The gray image is a code over GF(2) with n=68, k=13 and d=20.
This code was found by Heurico 1.16 in 0.396 seconds.