The generator matrix

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

generates a code of length 83 over F4[X]/(X^2) who´s minimum homogenous weight is 242.

Homogenous weight enumerator: w(x)=1x^0+564x^242+420x^243+75x^244+732x^246+600x^247+114x^248+468x^250+276x^251+24x^252+192x^254+48x^255+156x^258+60x^259+21x^260+60x^262+48x^263+12x^264+60x^266+60x^267+72x^270+24x^271+3x^272+6x^280

The gray image is a linear code over GF(4) with n=332, k=6 and d=242.
This code was found by Heurico 1.16 in 0.703 seconds.