The generator matrix

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

generates a code of length 93 over F4[X]/(X^2) who´s minimum homogenous weight is 262.

Homogenous weight enumerator: w(x)=1x^0+432x^262+768x^263+450x^264+756x^265+1932x^266+1896x^267+1284x^268+1248x^269+3240x^270+2724x^271+1413x^272+1572x^273+3744x^274+2928x^275+1596x^276+1848x^277+4056x^278+3300x^279+1737x^280+1824x^281+4068x^282+3228x^283+1479x^284+1668x^285+3228x^286+2604x^287+1218x^288+1044x^289+2496x^290+1656x^291+654x^292+576x^293+1032x^294+636x^295+345x^296+180x^297+336x^298+180x^299+51x^300+36x^301+12x^302+48x^303+12x^304

The gray image is a linear code over GF(4) with n=372, k=8 and d=262.
This code was found by Heurico 1.16 in 30.3 seconds.