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

generates a code of length 94 over F4[X]/(X^2) who´s minimum homogenous weight is 275.

Homogenous weight enumerator: w(x)=1x^0+744x^275+312x^276+1032x^279+396x^280+588x^283+60x^284+264x^287+87x^288+168x^291+81x^292+84x^295+48x^296+72x^299+24x^300+108x^303+12x^304+12x^307+3x^324

The gray image is a linear code over GF(4) with n=376, k=6 and d=275.
This code was found by Heurico 1.16 in 0.281 seconds.