The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 2X  1
 0  X  0 X+2 2X+2 3X+2  2  X 3X+2  0 2X 3X+2  2  2 3X  X 2X 2X X+2 2X+2 X+2
 0  0  2 2X+2 2X+2 2X 2X 2X+2  0 2X 2X+2  2  2  0  2 2X 2X  2 2X  2  2

generates a code of length 21 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+56x^19+98x^20+216x^21+88x^22+40x^23+4x^24+8x^25+1x^40

The gray image is a code over GF(2) with n=168, k=9 and d=76.
This code was found by Heurico 1.16 in 0.015 seconds.