The generator matrix

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

generates a code of length 82 over F4[X]/(X^2) who´s minimum homogenous weight is 228.

Homogenous weight enumerator: w(x)=1x^0+267x^228+432x^229+60x^230+600x^231+1476x^232+1272x^233+324x^234+1404x^235+2730x^236+2472x^237+348x^238+2196x^239+3876x^240+3756x^241+528x^242+2592x^243+4353x^244+3684x^245+540x^246+2988x^247+4650x^248+3672x^249+516x^250+2652x^251+4101x^252+3648x^253+420x^254+1836x^255+2541x^256+1740x^257+264x^258+936x^259+1104x^260+708x^261+72x^262+156x^263+387x^264+120x^265+39x^268+30x^272+18x^276+9x^280+9x^284+6x^288+3x^300

The gray image is a linear code over GF(4) with n=328, k=8 and d=228.
This code was found by Heurico 1.16 in 25.2 seconds.