The generator matrix

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

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+102x^52+396x^53+204x^56+732x^57+384x^60+1188x^61+279x^64+756x^65+30x^68+12x^72+12x^76

The gray image is a linear code over GF(4) with n=80, k=6 and d=52.
This code was found by Heurico 1.16 in 0.0229 seconds.