The generator matrix

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

generates a code of length 92 over F4[X]/(X^2) who´s minimum homogenous weight is 259.

Homogenous weight enumerator: w(x)=1x^0+384x^259+726x^260+612x^261+924x^262+1320x^263+2109x^264+1536x^265+1296x^266+2196x^267+3141x^268+1932x^269+1932x^270+2796x^271+3567x^272+2268x^273+1812x^274+2568x^275+3702x^276+2448x^277+2448x^278+2496x^279+3375x^280+2016x^281+1692x^282+2460x^283+3051x^284+1752x^285+1368x^286+1572x^287+1980x^288+912x^289+600x^290+828x^291+666x^292+288x^293+192x^294+204x^295+192x^296+36x^297+24x^298+60x^299+18x^300+24x^301+12x^303

The gray image is a linear code over GF(4) with n=368, k=8 and d=259.
This code was found by Heurico 1.16 in 32.7 seconds.