The generator matrix

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

generates a code of length 82 over F4[X]/(X^2) who´s minimum homogenous weight is 230.

Homogenous weight enumerator: w(x)=1x^0+852x^230+1647x^232+3408x^234+2928x^236+5880x^238+3603x^240+6600x^242+4620x^244+6480x^246+4503x^248+7128x^250+4020x^252+5268x^254+2778x^256+3048x^258+1164x^260+1188x^262+294x^264+72x^266+36x^268+12x^270+6x^272

The gray image is a linear code over GF(4) with n=328, k=8 and d=230.
This code was found by Heurico 1.16 in 37.3 seconds.