The generator matrix

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

generates a code of length 18 over F4[X]/(X^2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+12x^48+864x^50+960x^51+96x^52+576x^54+144x^56+864x^58+576x^59+3x^64

The gray image is a linear code over GF(4) with n=72, k=6 and d=48.
This code was found by Heurico 1.16 in 0.016 seconds.