The generator matrix

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

generates a code of length 18 over F4[X]/(X^2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+216x^50+240x^51+24x^52+144x^54+36x^56+216x^58+144x^59+3x^64

The gray image is a linear code over GF(4) with n=72, k=5 and d=50.
This code was found by Heurico 1.16 in 6.87e-008 seconds.