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

generates a code of length 85 over F4[X]/(X^2) who´s minimum homogenous weight is 248.

Homogenous weight enumerator: w(x)=1x^0+531x^248+264x^249+576x^251+1182x^252+264x^253+195x^256+48x^257+81x^260+183x^264+168x^265+192x^267+339x^268+24x^269+42x^272+3x^276+3x^284

The gray image is a linear code over GF(4) with n=340, k=6 and d=248.
This code was found by Heurico 1.16 in 0.258 seconds.