The generator matrix
1 0 1 1 1 0 1 1 2 1 1 X 1 1 1 X 1
0 1 1 0 X+1 1 0 X+3 1 X+1 X 1 3 X+2 3 X 2
0 0 X 0 0 X X 0 X X+2 X+2 2 X+2 X+2 2 0 0
0 0 0 X 0 X X X 2 X 0 X+2 X X 2 X X+2
0 0 0 0 2 0 0 0 2 2 0 0 2 0 0 2 2
0 0 0 0 0 2 0 0 0 0 0 0 2 2 2 2 2
0 0 0 0 0 0 2 2 0 2 2 0 0 2 0 2 0
generates a code of length 17 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 12.
Homogenous weight enumerator: w(x)=1x^0+224x^12+128x^13+640x^14+768x^15+1686x^16+1280x^17+1696x^18+768x^19+688x^20+128x^21+160x^22+24x^24+1x^32
The gray image is a code over GF(2) with n=68, k=13 and d=24.
This code was found by Heurico 1.16 in 15.7 seconds.