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

generates a code of length 84 over F4[X]/(X^2) who´s minimum homogenous weight is 236.

Homogenous weight enumerator: w(x)=1x^0+531x^236+1020x^237+732x^238+648x^239+1668x^240+3156x^241+1248x^242+984x^243+2307x^244+4140x^245+1548x^246+1284x^247+2895x^248+5064x^249+1860x^250+1284x^251+3138x^252+5280x^253+1980x^254+1296x^255+2841x^256+4620x^257+1464x^258+1140x^259+2595x^260+3456x^261+1140x^262+684x^263+1275x^264+1800x^265+612x^266+324x^267+501x^268+588x^269+168x^270+24x^271+168x^272+48x^273+12x^275+12x^277

The gray image is a linear code over GF(4) with n=336, k=8 and d=236.
This code was found by Heurico 1.16 in 81 seconds.