The generator matrix

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

generates a code of length 89 over F4[X]/(X^2) who´s minimum homogenous weight is 245.

Homogenous weight enumerator: w(x)=1x^0+324x^245+456x^246+612x^247+1191x^248+1908x^249+2016x^250+1860x^251+2913x^252+4152x^253+5520x^254+3468x^255+4833x^256+6588x^257+8076x^258+5376x^259+7239x^260+9564x^261+11400x^262+8016x^263+9591x^264+13104x^265+14988x^266+8868x^267+11244x^268+14052x^269+15012x^270+9084x^271+10104x^272+11328x^273+11760x^274+6672x^275+7389x^276+7548x^277+7368x^278+3780x^279+3528x^280+4044x^281+2652x^282+1200x^283+1128x^284+924x^285+564x^286+192x^287+168x^288+180x^289+60x^290+24x^291+9x^292+12x^293+9x^296+9x^300+6x^304+12x^308+9x^312+6x^316+3x^324

The gray image is a linear code over GF(4) with n=356, k=9 and d=245.
This code was found by Heurico 1.16 in 405 seconds.