The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+324x^49+672x^50+1008x^51+660x^52+1668x^53+2100x^54+3084x^55+1965x^56+4668x^57+4644x^58+5148x^59+5937x^60+9324x^61+7068x^62+5988x^63+3171x^64+3984x^65+2412x^66+1668x^67+18x^68+9x^72+9x^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 4.1 seconds.