The generator matrix

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

generates a code of length 21 over F4[X]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+396x^52+1584x^56+4050x^60+6369x^64+3744x^68+156x^72+66x^76+18x^80

The gray image is a linear code over GF(4) with n=84, k=7 and d=52.
This code was found by Heurico 1.16 in 61.5 seconds.