The generator matrix

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

generates a code of length 20 over F4[X]/(X^2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+198x^48+324x^49+900x^50+96x^51+1155x^52+1584x^53+2064x^54+864x^55+4671x^56+4824x^57+5688x^58+2592x^59+9279x^60+7344x^61+6480x^62+2592x^63+7002x^64+4356x^65+3300x^66+105x^68+93x^72+21x^76+3x^80

The gray image is a linear code over GF(4) with n=80, k=8 and d=48.
This code was found by Heurico 1.16 in 50.6 seconds.