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 a^2*X  1  1  1  1  1  1  1  1  X  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  X  1  0  1  X a^2*X+a  1 a*X a^2 a*X a^2*X+a^2
 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  1 a*X+a^2 a^2*X a*X+1 a*X+a^2  0  X a^2*X+a a^2*X+a  1 a*X
 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  X a^2*X  X  0  X a^2*X  X a^2*X  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+660x^247+111x^248+1620x^250+1212x^251+300x^252+1836x^254+1236x^255+114x^256+1632x^258+1056x^259+210x^260+1248x^262+768x^263+126x^264+936x^266+588x^267+72x^268+624x^270+372x^271+51x^272+468x^274+216x^275+18x^276+96x^278+36x^279+21x^280

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 3.2 seconds.