The generator matrix

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

generates a code of length 21 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+28x^16+48x^17+68x^18+176x^19+420x^20+576x^21+416x^22+176x^23+62x^24+48x^25+22x^26+4x^30+1x^32+2x^34

The gray image is a code over GF(2) with n=168, k=11 and d=64.
This code was found by Heurico 1.16 in 0.031 seconds.