The generator matrix
1 1 1 1 X 1 1 0 1 1 X X 1 1 1 1 1
0 X 0 X+2 X 0 X+2 X 0 X+2 X+2 X+2 0 0 0 0 0
0 0 2 0 0 0 0 0 0 0 2 0 2 2 0 0 0
0 0 0 2 0 0 0 0 0 0 2 2 2 0 0 0 0
0 0 0 0 2 0 0 0 0 0 2 2 0 2 0 0 0
0 0 0 0 0 2 0 0 0 2 2 0 0 2 0 0 0
0 0 0 0 0 0 2 0 0 2 0 2 2 0 0 0 0
0 0 0 0 0 0 0 2 0 2 0 2 0 2 0 0 0
0 0 0 0 0 0 0 0 2 2 2 0 2 0 0 0 0
generates a code of length 17 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 8.
Homogenous weight enumerator: w(x)=1x^0+63x^8+40x^10+176x^12+64x^13+230x^14+256x^15+1031x^16+384x^17+1016x^18+256x^19+224x^20+64x^21+196x^22+41x^24+48x^26+6x^30
The gray image is a code over GF(2) with n=68, k=12 and d=16.
This code was found by Heurico 1.16 in 0.0418 seconds.