The generator matrix

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

generates a code of length 94 over F4[X]/(X^2) who´s minimum homogenous weight is 274.

Homogenous weight enumerator: w(x)=1x^0+672x^274+462x^276+768x^278+93x^280+792x^282+216x^284+132x^286+51x^288+312x^290+150x^292+240x^294+6x^296+144x^298+36x^300+12x^302+9x^312

The gray image is a linear code over GF(4) with n=376, k=6 and d=274.
This code was found by Heurico 1.16 in 0.271 seconds.