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

generates a code of length 86 over F4[X]/(X^2) who´s minimum homogenous weight is 246.

Homogenous weight enumerator: w(x)=1x^0+756x^246+612x^247+165x^248+1692x^250+1176x^251+222x^252+1812x^254+1296x^255+117x^256+1596x^258+1164x^259+180x^260+1176x^262+696x^263+177x^264+972x^266+624x^267+78x^268+672x^270+336x^271+60x^272+384x^274+204x^275+24x^276+144x^278+36x^279+12x^282

The gray image is a linear code over GF(4) with n=344, k=7 and d=246.
This code was found by Heurico 1.16 in 4.83 seconds.