The generator matrix

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

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+204x^48+867x^52+3210x^56+6921x^60+4911x^64+165x^68+90x^72+15x^76

The gray image is a linear code over GF(4) with n=80, k=7 and d=48.
This code was found by Heurico 1.16 in 0.326 seconds.