The generator matrix

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

generates a code of length 85 over F4[X]/(X^2) who´s minimum homogenous weight is 238.

Homogenous weight enumerator: w(x)=1x^0+240x^238+420x^239+495x^240+876x^241+1752x^242+1596x^243+1374x^244+1416x^245+2724x^246+2352x^247+1878x^248+2064x^249+3276x^250+2892x^251+2328x^252+2628x^253+3768x^254+2808x^255+2418x^256+2496x^257+3792x^258+2520x^259+2181x^260+2064x^261+2808x^262+2124x^263+1539x^264+1476x^265+1956x^266+1584x^267+750x^268+648x^269+912x^270+480x^271+330x^272+144x^273+264x^274+96x^275+15x^276+12x^277+12x^278+24x^279+3x^280

The gray image is a linear code over GF(4) with n=340, k=8 and d=238.
This code was found by Heurico 1.16 in 27.2 seconds.