The generator matrix

 1  0  0  1  1  1  1  1  1  1 a^2*X  1 a^2*X  1  1  1  1  1  1  1  0
 0  1  0  0  X a^2*X  1 a^2*X+a a^2  1  1 a^2*X+a^2  1  a a^2*X+1 a^2*X+a^2 a^2 X+a  a a^2*X+1  1
 0  0  1  1 a^2*X+a a^2 a^2 X+a^2 X+a^2 X+1 X+a^2 a*X X+1  a X+a X+a X+1  X  1  0 X+a
 0  0  0 a^2*X a*X a*X  X  X a^2*X a^2*X  X  0  0 a*X  0  X  0 a*X  X a^2*X a^2*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+2124x^56+4032x^60+6111x^64+4032x^68+84x^72

The gray image is a linear code over GF(4) with n=84, k=7 and d=56.
This code was found by Heurico 1.16 in 42.2 seconds.