The generator matrix

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

generates a code of length 97 over F4[X]/(X^2) who´s minimum homogenous weight is 276.

Homogenous weight enumerator: w(x)=1x^0+621x^276+1881x^280+2373x^284+2664x^288+2745x^292+2880x^296+1887x^300+936x^304+240x^308+60x^312+24x^316+15x^320+21x^324+18x^328+6x^332+3x^336+3x^340+3x^344+3x^352

The gray image is a linear code over GF(4) with n=388, k=7 and d=276.
This code was found by Heurico 1.16 in 9.15 seconds.