The generator matrix

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

generates a code of length 87 over F4[X]/(X^2) who´s minimum homogenous weight is 240.

Homogenous weight enumerator: w(x)=1x^0+507x^240+900x^241+1164x^242+504x^243+2757x^244+3132x^245+3408x^246+1392x^247+5853x^248+5124x^249+6084x^250+2268x^251+8949x^252+8040x^253+9144x^254+3228x^255+13200x^256+11040x^257+12360x^258+4392x^259+16416x^260+14460x^261+13320x^262+4704x^263+16767x^264+13188x^265+13944x^266+4284x^267+13995x^268+9996x^269+8772x^270+2556x^271+7668x^272+5556x^273+3948x^274+984x^275+3189x^276+1848x^277+1344x^278+216x^279+669x^280+384x^281+228x^282+48x^283+90x^284+60x^285+12x^286+33x^288+3x^292+3x^296+6x^300+3x^304+3x^308

The gray image is a linear code over GF(4) with n=348, k=9 and d=240.
This code was found by Heurico 1.16 in 460 seconds.