The generator matrix
1 1 1 1 X X X 1 1 1 1 X X X 1 1 1
0 X 0 X 0 X X 0 0 X X+2 0 X X+2 0 0 0
0 0 X X X X 0 0 X+2 X 0 X+2 X+2 0 0 0 0
0 0 0 2 0 0 0 0 0 0 2 0 2 2 0 0 0
0 0 0 0 2 0 0 0 0 2 2 2 2 2 0 0 0
0 0 0 0 0 2 0 0 0 2 0 2 2 0 0 0 0
0 0 0 0 0 0 2 0 0 2 0 2 0 2 0 0 0
0 0 0 0 0 0 0 2 0 2 2 0 2 0 0 0 0
0 0 0 0 0 0 0 0 2 0 2 2 0 2 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+87x^8+80x^10+16x^11+416x^12+480x^13+182x^14+1008x^15+263x^16+3136x^17+248x^18+1008x^19+176x^20+480x^21+436x^22+16x^23+81x^24+72x^26+6x^30
The gray image is a code over GF(2) with n=68, k=13 and d=16.
This code was found by Heurico 1.16 in 0.215 seconds.