The generator matrix

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

generates a code of length 20 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+93x^48+177x^52+168x^56+3219x^60+195x^64+135x^68+84x^72+21x^76+3x^80

The gray image is a linear code over GF(4) with n=80, k=6 and d=48.
This code was found by Heurico 1.16 in 0.0419 seconds.