The generator matrix

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

generates a code of length 72 over F4[X]/(X^2) who´s minimum homogenous weight is 204.

Homogenous weight enumerator: w(x)=1x^0+432x^204+516x^205+432x^206+1179x^208+1116x^209+612x^210+1617x^212+1380x^213+612x^214+1239x^216+1200x^217+564x^218+1149x^220+888x^221+372x^222+780x^224+588x^225+264x^226+522x^228+276x^229+168x^230+201x^232+168x^233+48x^234+45x^236+12x^237+3x^244

The gray image is a linear code over GF(4) with n=288, k=7 and d=204.
This code was found by Heurico 1.16 in 1.33 seconds.