The generator matrix

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

generates a code of length 20 over F4[X]/(X^2) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+588x^51+240x^52+2016x^55+924x^56+4248x^59+1632x^60+4608x^63+1215x^64+828x^67+48x^68+36x^72

The gray image is a linear code over GF(4) with n=80, k=7 and d=51.
This code was found by Heurico 1.16 in 0.235 seconds.