The generator matrix

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

generates a code of length 75 over F4[X]/(X^2) who´s minimum homogenous weight is 216.

Homogenous weight enumerator: w(x)=1x^0+30x^216+48x^219+66x^220+288x^223+39x^224+432x^227+57x^228+42x^232+18x^236+3x^292

The gray image is a linear code over GF(4) with n=300, k=5 and d=216.
This code was found by Heurico 1.16 in 0.078 seconds.