The generator matrix

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

generates a code of length 20 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+240x^49+948x^50+948x^51+666x^52+1284x^53+2592x^54+2532x^55+1947x^56+3732x^57+6696x^58+5148x^59+5958x^60+6924x^61+9600x^62+5196x^63+3159x^64+3180x^65+3204x^66+1536x^67+18x^68+15x^72+6x^76+6x^80

The gray image is a linear code over GF(4) with n=80, k=8 and d=49.
This code was found by Heurico 1.16 in 6.59 seconds.