The generator matrix

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

generates a code of length 19 over F4[X]/(X^2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+105x^48+780x^52+1368x^56+1695x^60+120x^64+18x^68+6x^72+3x^76

The gray image is a linear code over GF(4) with n=76, k=6 and d=48.
This code was found by Heurico 1.16 in 0.0216 seconds.