The generator matrix

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

generates a code of length 20 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+228x^46+420x^47+465x^48+1188x^49+2268x^50+2724x^51+2889x^52+5808x^53+9864x^54+7560x^55+9669x^56+19224x^57+29400x^58+16680x^59+18459x^60+31536x^61+39636x^62+16980x^63+14520x^64+15972x^65+10764x^66+4788x^67+999x^68+75x^72+21x^76+6x^80

The gray image is a linear code over GF(4) with n=80, k=9 and d=46.
This code was found by Heurico 1.16 in 46.1 seconds.