The generator matrix

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

generates a code of length 94 over F4[X]/(X^2) who´s minimum homogenous weight is 276.

Homogenous weight enumerator: w(x)=1x^0+93x^276+192x^279+66x^280+576x^283+36x^284+33x^288+6x^296+12x^300+6x^304+3x^372

The gray image is a linear code over GF(4) with n=376, k=5 and d=276.
This code was found by Heurico 1.16 in 0.188 seconds.