The generator matrix

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

generates a code of length 20 over F4[X]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+264x^52+1536x^53+900x^56+3072x^57+1584x^60+4608x^61+1263x^64+3072x^65+72x^68+12x^72

The gray image is a linear code over GF(4) with n=80, k=7 and d=52.
This code was found by Heurico 1.16 in 18.6 seconds.