The generator matrix

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

generates a code of length 91 over F4[X]/(X^2) who´s minimum homogenous weight is 256.

Homogenous weight enumerator: w(x)=1x^0+402x^256+408x^257+684x^258+996x^259+1920x^260+1176x^261+1164x^262+2148x^263+3069x^264+1848x^265+1920x^266+2676x^267+3126x^268+2412x^269+1776x^270+2760x^271+3867x^272+2352x^273+2184x^274+2832x^275+3417x^276+2244x^277+1908x^278+2460x^279+3213x^280+1764x^281+1536x^282+1788x^283+1992x^284+1092x^285+732x^286+936x^287+1146x^288+432x^289+336x^290+252x^291+321x^292+84x^293+36x^294+48x^295+54x^296+12x^297+12x^298

The gray image is a linear code over GF(4) with n=364, k=8 and d=256.
This code was found by Heurico 1.16 in 29.5 seconds.