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

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+366x^268+900x^269+780x^270+588x^271+1413x^272+2040x^273+1848x^274+1152x^275+2184x^276+2832x^277+2652x^278+1452x^279+2820x^280+3420x^281+2460x^282+1560x^283+3090x^284+3468x^285+3024x^286+1440x^287+2931x^288+3288x^289+2508x^290+1368x^291+2280x^292+2592x^293+1896x^294+972x^295+1734x^296+1812x^297+1176x^298+444x^299+804x^300+900x^301+408x^302+192x^303+258x^304+228x^305+120x^306+36x^307+36x^308+12x^309+24x^310+12x^311+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 31.9 seconds.