The generator matrix

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

generates a code of length 21 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+528x^54+603x^56+2160x^58+888x^60+4176x^62+1602x^64+4560x^66+936x^68+864x^70+57x^72+9x^80

The gray image is a linear code over GF(4) with n=84, k=7 and d=54.
This code was found by Heurico 1.16 in 0.827 seconds.