The generator matrix

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

generates a code of length 86 over F4[X]/(X^2) who´s minimum homogenous weight is 240.

Homogenous weight enumerator: w(x)=1x^0+189x^240+720x^241+252x^242+132x^243+1290x^244+2196x^245+840x^246+300x^247+2193x^248+3888x^249+1056x^250+504x^251+2919x^252+5280x^253+1584x^254+408x^255+3312x^256+6144x^257+1692x^258+624x^259+2991x^260+6060x^261+1608x^262+504x^263+3069x^264+5232x^265+1176x^266+360x^267+2121x^268+2856x^269+816x^270+120x^271+960x^272+1200x^273+144x^274+108x^275+288x^276+216x^277+48x^278+12x^279+48x^280+15x^284+21x^288+18x^292+12x^296+3x^300+3x^304+3x^308

The gray image is a linear code over GF(4) with n=344, k=8 and d=240.
This code was found by Heurico 1.16 in 26.5 seconds.