The generator matrix

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

generates a code of length 20 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+261x^52+882x^56+1623x^60+1275x^64+27x^68+18x^72+9x^76

The gray image is a linear code over GF(4) with n=80, k=6 and d=52.
This code was found by Heurico 1.16 in 0.0236 seconds.