The generator matrix

 1  0  0  0  1  1  1  X  1  1  0  X  1  1  1  1 aX  1  1  1
 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 X+a (a+1)X (a+1)X+1 a+1  0
 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 aX  1 X+1 X+1  a
 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 (a+1)X+a  1 (a+1)X+1 aX+a X+a+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+348x^49+744x^50+912x^51+621x^52+1560x^53+2328x^54+2856x^55+1791x^56+5232x^57+4968x^58+4680x^59+4869x^60+10344x^61+7752x^62+5304x^63+2916x^64+4020x^65+2640x^66+1608x^67+15x^68+9x^72+15x^76+3x^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 5.23 seconds.