The generator matrix

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

generates a code of length 85 over F4[X]/(X^2) who´s minimum homogenous weight is 234.

Homogenous weight enumerator: w(x)=1x^0+480x^234+816x^235+849x^236+972x^237+2664x^238+2676x^239+2121x^240+2496x^241+5100x^242+5844x^243+4500x^244+4104x^245+9264x^246+9528x^247+6453x^248+5640x^249+12084x^250+12180x^251+9039x^252+7560x^253+15708x^254+15060x^255+10716x^256+7884x^257+16104x^258+14400x^259+9447x^260+7284x^261+13200x^262+11484x^263+6492x^264+4608x^265+8292x^266+5604x^267+2532x^268+1908x^269+2532x^270+2040x^271+828x^272+492x^273+564x^274+228x^275+186x^276+60x^277+24x^278+12x^279+21x^280+21x^284+15x^288+15x^292+6x^296+3x^300+3x^304

The gray image is a linear code over GF(4) with n=340, k=9 and d=234.
This code was found by Heurico 1.16 in 413 seconds.