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

generates a code of length 72 over F4[X]/(X^2) who´s minimum homogenous weight is 208.

Homogenous weight enumerator: w(x)=1x^0+210x^208+276x^209+396x^210+180x^211+462x^212+372x^213+336x^214+60x^215+294x^216+216x^217+168x^218+84x^219+147x^220+60x^221+84x^222+24x^223+171x^224+120x^225+60x^226+12x^227+60x^228+96x^229+84x^230+12x^231+60x^232+12x^233+24x^234+12x^235+3x^252

The gray image is a linear code over GF(4) with n=288, k=6 and d=208.
This code was found by Heurico 1.16 in 0.109 seconds.