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

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+753x^248+480x^250+996x^252+372x^254+432x^256+96x^258+252x^260+60x^262+189x^264+84x^266+156x^268+24x^270+102x^272+12x^274+60x^276+24x^278+3x^288

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 1.05 seconds.