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

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+624x^234+684x^235+111x^236+1656x^238+1140x^239+240x^240+1884x^242+1356x^243+198x^244+1620x^246+984x^247+219x^248+1392x^250+744x^251+102x^252+984x^254+552x^255+51x^256+612x^258+480x^259+66x^260+348x^262+156x^263+30x^264+96x^266+48x^267+3x^268+3x^280

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 1.27 seconds.