The generator matrix

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

generates a code of length 95 over F4[X]/(X^2) who´s minimum homogenous weight is 278.

Homogenous weight enumerator: w(x)=1x^0+600x^278+612x^279+105x^280+708x^282+372x^283+48x^284+444x^286+216x^287+27x^288+192x^290+120x^291+33x^292+168x^294+48x^295+27x^296+48x^298+96x^299+12x^300+60x^302+36x^303+84x^306+36x^307+3x^308

The gray image is a linear code over GF(4) with n=380, k=6 and d=278.
This code was found by Heurico 1.16 in 4.31 seconds.