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

generates a code of length 84 over F4[X]/(X^2) who´s minimum homogenous weight is 245.

Homogenous weight enumerator: w(x)=1x^0+408x^245+612x^246+228x^247+18x^248+612x^249+480x^250+180x^251+21x^252+300x^253+288x^254+60x^255+168x^257+120x^258+48x^259+9x^260+48x^261+60x^262+36x^263+9x^264+96x^265+96x^266+12x^267+3x^268+36x^269+48x^270+12x^271+60x^273+24x^274+3x^284

The gray image is a linear code over GF(4) with n=336, k=6 and d=245.
This code was found by Heurico 1.16 in 1.17 seconds.