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

generates a code of length 85 over F4[X]/(X^2) who´s minimum homogenous weight is 236.

Homogenous weight enumerator: w(x)=1x^0+240x^236+156x^237+144x^238+300x^239+1431x^240+660x^241+492x^242+900x^243+3519x^244+1248x^245+744x^246+1692x^247+4506x^248+1704x^249+948x^250+2028x^251+5994x^252+2280x^253+1008x^254+2364x^255+6330x^256+2376x^257+1044x^258+2172x^259+5895x^260+1704x^261+696x^262+1716x^263+4020x^264+1560x^265+732x^266+804x^267+2064x^268+540x^269+288x^270+264x^271+624x^272+36x^273+48x^274+48x^275+102x^276+24x^277+24x^280+21x^284+15x^288+12x^292+6x^296+9x^300+3x^304

The gray image is a linear code over GF(4) with n=340, k=8 and d=236.
This code was found by Heurico 1.16 in 26.2 seconds.