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.