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

generates a code of length 86 over F4[X]/(X^2) who´s minimum homogenous weight is 251.

Homogenous weight enumerator: w(x)=1x^0+660x^251+360x^252+1164x^255+264x^256+552x^259+174x^260+192x^263+84x^264+216x^267+72x^268+144x^271+12x^272+60x^275+18x^276+84x^279+36x^280+3x^288

The gray image is a linear code over GF(4) with n=344, k=6 and d=251.
This code was found by Heurico 1.16 in 0.187 seconds.