The generator matrix

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

generates a code of length 75 over F4[X]/(X^2) who´s minimum homogenous weight is 217.

Homogenous weight enumerator: w(x)=1x^0+264x^217+192x^218+348x^219+363x^220+360x^221+348x^222+240x^223+228x^224+312x^225+168x^226+144x^227+63x^228+168x^229+96x^230+108x^231+72x^232+84x^233+96x^234+48x^235+42x^236+72x^237+36x^238+36x^239+36x^240+84x^241+24x^242+36x^243+24x^244+3x^264

The gray image is a linear code over GF(4) with n=300, k=6 and d=217.
This code was found by Heurico 1.16 in 0.125 seconds.