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.