The generator matrix

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

generates a code of length 20 over F4[X]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+300x^54+783x^56+828x^58+600x^60+324x^62+789x^64+468x^66+3x^72

The gray image is a linear code over GF(4) with n=80, k=6 and d=54.
This code was found by Heurico 1.16 in 0.032 seconds.