The generator matrix

 1  0  0  0  1  1  1  1  1  0  1  1  1 a^2*X  1 a^2*X  1  1  1  1
 0  1  0  0  0  X  X a^2*X+1 a^2*X+1  1 a*X+1 a^2*X+a a^2  1  a  1 a^2*X+a a*X+a a*X+1 a^2*X+a
 0  0  1  0  1 a^2*X+a a^2*X+a^2  a  0  a a*X+a^2  X  a  1 a*X+a^2 a^2 a*X+a a*X a*X+a a*X+a
 0  0  0  1 a^2  a  1 a*X  a  a a^2*X+a^2 a^2*X+1 X+1  0 a^2*X a^2*X+a a*X+1  X a^2*X+a a*X+1
 0  0  0  0  X  0 a*X  0  X a*X a^2*X a*X  X a^2*X a*X  0 a^2*X a^2*X a^2*X  X

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

Homogenous weight enumerator: w(x)=1x^0+228x^46+384x^47+666x^48+960x^49+3012x^50+2472x^51+2295x^52+4800x^53+10776x^54+9216x^55+8724x^56+15936x^57+27960x^58+22800x^59+21711x^60+26688x^61+36804x^62+22464x^63+12207x^64+13056x^65+13380x^66+4104x^67+1413x^68+60x^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 49.2 seconds.