The generator matrix

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

generates a code of length 83 over F4[X]/(X^2) who´s minimum homogenous weight is 241.

Homogenous weight enumerator: w(x)=1x^0+420x^241+450x^244+1368x^245+270x^248+528x^249+81x^252+18x^256+180x^257+180x^260+456x^261+12x^264+120x^265+9x^268+3x^272

The gray image is a linear code over GF(4) with n=332, k=6 and d=241.
This code was found by Heurico 1.16 in 9.81 seconds.