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

generates a code of length 72 over F4[X]/(X^2) who´s minimum homogenous weight is 209.

Homogenous weight enumerator: w(x)=1x^0+384x^209+552x^210+276x^211+9x^212+588x^213+552x^214+144x^215+27x^216+264x^217+276x^218+48x^219+21x^220+240x^221+132x^222+24x^223+144x^225+48x^226+24x^227+36x^229+108x^230+48x^231+72x^233+60x^234+12x^235+3x^236+3x^252

The gray image is a linear code over GF(4) with n=288, k=6 and d=209.
This code was found by Heurico 1.16 in 43.5 seconds.