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

generates a code of length 95 over F4[X]/(X^2) who´s minimum homogenous weight is 268.

Homogenous weight enumerator: w(x)=1x^0+372x^268+828x^269+792x^270+564x^271+1593x^272+1932x^273+1920x^274+1248x^275+1992x^276+2784x^277+2712x^278+1428x^279+2751x^280+3780x^281+2472x^282+1476x^283+3012x^284+3348x^285+2712x^286+1596x^287+3210x^288+3180x^289+2532x^290+1140x^291+2208x^292+2808x^293+1968x^294+960x^295+1647x^296+1956x^297+1164x^298+576x^299+768x^300+708x^301+492x^302+204x^303+291x^304+132x^305+120x^306+24x^307+72x^308+36x^309+12x^310+12x^313+3x^320

The gray image is a linear code over GF(4) with n=380, k=8 and d=268.
This code was found by Heurico 1.16 in 32.9 seconds.