The generator matrix

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

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+78x^48+72x^52+768x^54+54x^56+24x^60+9x^64+18x^72

The gray image is a linear code over GF(4) with n=72, k=5 and d=48.
This code was found by Heurico 1.16 in 0.016 seconds.