The generator matrix

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

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+150x^52+153x^56+192x^57+201x^60+1152x^61+150x^64+1728x^65+135x^68+135x^72+87x^76+9x^80+3x^84

The gray image is a linear code over GF(4) with n=84, k=6 and d=52.
This code was found by Heurico 1.16 in 0.0696 seconds.