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 a*X  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  1 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 X+1  0 a^2*X
 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 a^2*X  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+546x^204+804x^206+1749x^208+1212x^210+2340x^212+1344x^214+1869x^216+1032x^218+1491x^220+864x^222+1158x^224+504x^226+693x^228+300x^230+327x^232+84x^234+63x^236+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 1.19 seconds.