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.