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

generates a code of length 94 over F4[X]/(X^2) who´s minimum homogenous weight is 265.

Homogenous weight enumerator: w(x)=1x^0+384x^265+612x^266+864x^267+807x^268+1608x^269+1632x^270+1824x^271+1320x^272+2652x^273+2016x^274+2592x^275+2007x^276+3144x^277+2868x^278+2568x^279+1887x^280+3144x^281+2880x^282+2748x^283+1806x^284+3192x^285+2520x^286+2664x^287+1809x^288+2688x^289+2280x^290+1872x^291+1311x^292+1812x^293+1332x^294+1140x^295+495x^296+948x^297+636x^298+504x^299+309x^300+372x^301+96x^302+108x^303+24x^304+24x^305+24x^306+12x^307

The gray image is a linear code over GF(4) with n=376, k=8 and d=265.
This code was found by Heurico 1.16 in 31 seconds.