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.