The generator matrix

 1  1  1  1  1  1  1  1  X  1  1  1  X  0  1  X  1
 0  X  0  0  0  0  0  X X+2 X+2  X X+2  2  0  X X+2  0
 0  0  X  0  0  0  X  0  X X+2 X+2 X+2  X  2  X  0  0
 0  0  0  X  0  X  X  X  0  2 X+2 X+2  2  X  0  X  0
 0  0  0  0  X  X  0  2 X+2  X  X  0  2  2  0 X+2  0
 0  0  0  0  0  2  0  0  2  2  0  2  2  0  2  2  0
 0  0  0  0  0  0  2  2  2  0  0  2  2  0  0  0  0

generates a code of length 17 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+77x^10+62x^11+177x^12+238x^13+576x^14+426x^15+2231x^16+570x^17+2246x^18+482x^19+604x^20+210x^21+160x^22+54x^23+56x^24+6x^25+13x^26+3x^28

The gray image is a code over GF(2) with n=68, k=13 and d=20.
This code was found by Heurico 1.16 in 0.455 seconds.