The generator matrix

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

generates a code of length 95 over F4[X]/(X^2) who´s minimum homogenous weight is 281.

Homogenous weight enumerator: w(x)=1x^0+156x^281+216x^282+30x^284+96x^285+288x^286+18x^288+108x^289+72x^290+3x^292+24x^293+3x^296+3x^300+6x^312

The gray image is a linear code over GF(4) with n=380, k=5 and d=281.
This code was found by Heurico 1.16 in 0.156 seconds.