The generator matrix

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

generates a code of length 81 over F4[X]/(X^2) who´s minimum homogenous weight is 227.

Homogenous weight enumerator: w(x)=1x^0+600x^227+588x^228+1092x^229+444x^230+2424x^231+1032x^232+2376x^233+612x^234+4068x^235+1701x^236+3336x^237+732x^238+5124x^239+1983x^240+3204x^241+636x^242+4932x^243+2103x^244+3456x^245+840x^246+4884x^247+2034x^248+3168x^249+660x^250+4236x^251+1362x^252+2088x^253+468x^254+2124x^255+714x^256+948x^257+204x^258+756x^259+243x^260+300x^261+12x^262+36x^263+12x^264+3x^268

The gray image is a linear code over GF(4) with n=324, k=8 and d=227.
This code was found by Heurico 1.16 in 73.9 seconds.