The generator matrix

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

generates a code of length 21 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+18x^20+96x^21+6x^22+5x^24+2x^30

The gray image is a code over GF(2) with n=168, k=7 and d=80.
This code was found by Heurico 1.16 in 6.87e-008 seconds.