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.