The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 2X+2 X X 1
0 2 0 2 0 2 2X 2X+2 0 2 2X 2X+2 2X 2X+2 2X 2X+2 2 2 0 0 0
0 0 2X 0 0 2X 2X 2X 2X 2X 2X 0 0 2X 0 0 0 0 2X 0 0
0 0 0 2X 2X 2X 2X 0 2X 0 0 2X 2X 2X 0 0 0 2X 2X 0 0
generates a code of length 21 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 18.
Homogenous weight enumerator: w(x)=1x^0+7x^18+2x^19+78x^20+78x^21+72x^22+14x^23+1x^24+2x^25+1x^34
The gray image is a code over GF(2) with n=168, k=8 and d=72.
This code was found by Heurico 1.16 in 1.05e-007 seconds.