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

generates a code of length 91 over F4[X]/(X^2) who´s minimum homogenous weight is 251.

Homogenous weight enumerator: w(x)=1x^0+384x^251+576x^252+624x^253+996x^254+1728x^255+2469x^256+2028x^257+2700x^258+4092x^259+5670x^260+3516x^261+4536x^262+6816x^263+8688x^264+5460x^265+7152x^266+10332x^267+12237x^268+7788x^269+8556x^270+12648x^271+14586x^272+9120x^273+9984x^274+12816x^275+15969x^276+8400x^277+10116x^278+11724x^279+12165x^280+6480x^281+6732x^282+8460x^283+7551x^284+4092x^285+3408x^286+3552x^287+3126x^288+1380x^289+972x^290+972x^291+780x^292+252x^293+132x^294+204x^295+84x^296+12x^297+12x^298+21x^300+15x^304+9x^308+12x^312+3x^316+3x^320+3x^328

The gray image is a linear code over GF(4) with n=364, k=9 and d=251.
This code was found by Heurico 1.16 in 418 seconds.