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

generates a code of length 78 over F4[X]/(X^2) who´s minimum homogenous weight is 213.

Homogenous weight enumerator: w(x)=1x^0+348x^213+480x^214+600x^215+1359x^216+1944x^217+2136x^218+2076x^219+3702x^220+4128x^221+4656x^222+3768x^223+6435x^224+7176x^225+7812x^226+5784x^227+10113x^228+11196x^229+10728x^230+8712x^231+12969x^232+13872x^233+13188x^234+10128x^235+14217x^236+15096x^237+13200x^238+9204x^239+11940x^240+11700x^241+9468x^242+5832x^243+7530x^244+6000x^245+4632x^246+2520x^247+2667x^248+1968x^249+1188x^250+468x^251+591x^252+288x^253+96x^254+60x^255+78x^256+12x^257+27x^260+33x^264+3x^268+6x^272+6x^276+3x^284

The gray image is a linear code over GF(4) with n=312, k=9 and d=213.
This code was found by Heurico 1.16 in 338 seconds.