The generator matrix
1 0 0 0 0 1 1 1 1 2 1 2 1 X 2 1 X+2
0 1 0 0 0 2 1 3 X+3 1 2 1 X+2 2 X 0 X
0 0 1 0 0 X+3 X+1 X+2 X X+3 X 3 1 1 1 2 0
0 0 0 1 0 1 X 3 X 3 X+3 X+2 1 3 X+1 1 1
0 0 0 0 1 1 2 2 3 X+1 X+1 3 X+2 X X+3 X+2 X+3
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+571x^12+788x^13+2634x^14+3020x^15+6906x^16+4712x^17+7196x^18+3000x^19+2741x^20+708x^21+378x^22+60x^23+53x^24
The gray image is a code over GF(2) with n=68, k=15 and d=24.
This code was found by Heurico 1.13 in 72.8 seconds.