The generator matrix

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

generates a code of length 73 over F4[X]/(X^2) who´s minimum homogenous weight is 204.

Homogenous weight enumerator: w(x)=1x^0+270x^204+84x^205+180x^207+957x^208+300x^209+396x^211+1680x^212+516x^213+564x^215+1686x^216+552x^217+600x^219+2055x^220+732x^221+828x^223+1839x^224+540x^225+444x^227+1176x^228+300x^229+60x^231+348x^232+48x^233+90x^236+51x^240+36x^244+21x^248+12x^252+6x^256+6x^260+3x^264+3x^268

The gray image is a linear code over GF(4) with n=292, k=7 and d=204.
This code was found by Heurico 1.16 in 1.66 seconds.