The generator matrix

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

generates a code of length 79 over F4[X]/(X^2) who´s minimum homogenous weight is 216.

Homogenous weight enumerator: w(x)=1x^0+354x^216+504x^217+348x^218+1416x^219+2343x^220+2340x^221+1404x^222+3996x^223+5034x^224+4536x^225+2712x^226+7044x^227+8169x^228+7128x^229+3840x^230+10848x^231+13122x^232+11124x^233+5280x^234+14952x^235+15249x^236+13476x^237+5280x^238+16200x^239+16578x^240+13608x^241+5676x^242+13800x^243+12999x^244+8988x^245+3936x^246+8256x^247+7017x^248+4476x^249+1788x^250+2880x^251+2601x^252+1176x^253+420x^254+444x^255+402x^256+216x^257+36x^258+36x^259+48x^260+12x^261+21x^264+9x^268+12x^272+6x^276+3x^288

The gray image is a linear code over GF(4) with n=316, k=9 and d=216.
This code was found by Heurico 1.16 in 345 seconds.