The generator matrix
1 1 1 1 1 1 1 1 X X X X 2 2 2 2 1
0 2 0 2 0 0 2 2 0 2 2 0 0 2 2 0 0
0 0 2 2 0 2 2 0 2 2 0 0 2 2 0 0 0
generates a code of length 17 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 16.
Homogenous weight enumerator: w(x)=1x^0+3x^16+20x^17+4x^18+4x^21
The gray image is a code over GF(2) with n=68, k=5 and d=32.
This code was found by Heurico 1.16 in 0.000905 seconds.