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

generates a code of length 82 over F4[X]/(X^2) who´s minimum homogenous weight is 239.

Homogenous weight enumerator: w(x)=1x^0+732x^239+288x^240+1104x^243+318x^244+444x^247+216x^248+288x^251+108x^252+216x^255+15x^256+132x^259+36x^260+96x^263+24x^264+60x^267+12x^268+6x^276

The gray image is a linear code over GF(4) with n=328, k=6 and d=239.
This code was found by Heurico 1.16 in 0.25 seconds.