The generator matrix
1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 X X 1 1 1
0 1 1 a (a+1)X+a+1 0 (a+1)X+1 a (a+1)X+a+1 1 0 a (a+1)X+1 1 (a+1)X+a+1 X+a 1 X X aX+1 X+a+1
0 0 (a+1)X 0 X X (a+1)X X (a+1)X X 0 0 X X 0 (a+1)X aX X aX 0 aX
0 0 0 X aX X aX (a+1)X (a+1)X 0 X (a+1)X 0 aX aX (a+1)X 0 (a+1)X X 0 aX
generates a code of length 21 over F4[X,sigma]/(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 0.0228 seconds.