The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  1  0  1  1  X  1  1  X
 0  1  1  a a^2*X+a^2  0 a^2*X+1  a a^2*X+a^2  1  0  a a^2*X+1 a^2*X+a^2  1  X a*X+1  X X+a X+a^2  1
 0  0 a^2*X  0  X  0  X a*X a*X a*X a*X  X a^2*X a^2*X  0 a^2*X  0 a*X a^2*X  0 a^2*X
 0  0  0  X a*X a*X  0 a*X  X  X  0  X a*X  X  X  0  0  X  X  X  X

generates a code of length 21 over F4[X]/(X^2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+570x^56+960x^60+1557x^64+960x^68+30x^72+18x^80

The gray image is a linear code over GF(4) with n=84, k=6 and d=56.
This code was found by Heurico 1.16 in 0.0239 seconds.