The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X  0  0  0  X  0 a*X a*X  X a^2*X a^2*X  X a*X  X  0  0 a^2*X  X  0
 0  0  X  0  0 a^2*X  X  0 a*X a*X a*X  X a^2*X  0 a^2*X a*X  X a*X a*X  X
 0  0  0  X  0  X a^2*X a^2*X a*X  0 a*X  X  0  X a^2*X a^2*X  0 a^2*X  0 a*X
 0  0  0  0  X a^2*X a*X  X a^2*X  X  0  X a^2*X a*X a*X  X a*X  X a^2*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+93x^48+177x^52+168x^56+3219x^60+195x^64+135x^68+84x^72+21x^76+3x^80

The gray image is a linear code over GF(4) with n=80, k=6 and d=48.
This code was found by Heurico 1.16 in 0.042 seconds.