The generator matrix

 1  0  1  1  1  1  1  1  0  1  1  1  1  1  0  1  1  1  1  1  1
 0  1  1  a a+1  0 (a+1)X+1  a  1 (a+1)X+a+1 (a+1)X+1  a  0 (a+1)X+a+1  1 (a+1)X+1  0  a  X (a+1)X+1 X+a
 0  0 (a+1)X  0  0  0  X aX aX  X  X  X  X  0  0 aX (a+1)X (a+1)X  0 aX  X
 0  0  0  X  0  X (a+1)X  X aX aX aX (a+1)X  0 aX (a+1)X  X (a+1)X aX  X aX  X
 0  0  0  0 (a+1)X (a+1)X (a+1)X aX  X  0 aX  X  X (a+1)X  X (a+1)X (a+1)X  0  0 (a+1)X  0

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

Homogenous weight enumerator: w(x)=1x^0+321x^52+96x^54+927x^56+864x^58+2628x^60+2592x^62+3807x^64+2592x^66+2313x^68+159x^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 88.4 seconds.