The generator matrix

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

generates a code of length 82 over F4[X]/(X^2) who´s minimum homogenous weight is 234.

Homogenous weight enumerator: w(x)=1x^0+648x^234+696x^235+156x^236+1644x^238+1104x^239+141x^240+1920x^242+1248x^243+258x^244+1704x^246+1044x^247+174x^248+1188x^250+948x^251+150x^252+960x^254+492x^255+75x^256+636x^258+396x^259+33x^260+444x^262+192x^263+30x^264+72x^266+24x^267+3x^272+3x^276

The gray image is a linear code over GF(4) with n=328, k=7 and d=234.
This code was found by Heurico 1.16 in 1.64 seconds.