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

generates a code of length 94 over F4[X]/(X^2) who´s minimum homogenous weight is 278.

Homogenous weight enumerator: w(x)=1x^0+216x^278+168x^279+18x^280+144x^282+144x^283+27x^284+216x^286+72x^287+6x^292+9x^296+3x^308

The gray image is a linear code over GF(4) with n=376, k=5 and d=278.
This code was found by Heurico 1.16 in 0.328 seconds.