The generator matrix

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

generates a code of length 84 over F4[X]/(X^2) who´s minimum homogenous weight is 231.

Homogenous weight enumerator: w(x)=1x^0+516x^231+798x^232+600x^233+720x^234+2988x^235+3168x^236+1296x^237+2076x^238+6948x^239+5226x^240+3000x^241+3552x^242+11388x^243+8646x^244+4908x^245+4680x^246+16416x^247+12387x^248+6180x^249+6924x^250+20820x^251+14721x^252+7260x^253+6912x^254+20616x^255+14169x^256+6300x^257+6108x^258+16116x^259+11043x^260+4884x^261+3816x^262+10524x^263+5373x^264+1908x^265+1668x^266+3552x^267+1968x^268+468x^269+372x^270+660x^271+234x^272+60x^273+36x^274+48x^275+42x^276+24x^280+6x^284+6x^288+3x^292+3x^300+6x^304

The gray image is a linear code over GF(4) with n=336, k=9 and d=231.
This code was found by Heurico 1.16 in 379 seconds.