The generator matrix

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

generates a code of length 85 over F4[X]/(X^2) who´s minimum homogenous weight is 239.

Homogenous weight enumerator: w(x)=1x^0+1320x^239+600x^240+4392x^243+1734x^244+6612x^247+2532x^248+7896x^251+2616x^252+8892x^255+2910x^256+8148x^259+2592x^260+6276x^263+1980x^264+3840x^267+1056x^268+1548x^271+294x^272+204x^275+66x^276+24x^279+3x^288

The gray image is a linear code over GF(4) with n=340, k=8 and d=239.
This code was found by Heurico 1.16 in 759 seconds.