The generator matrix

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

generates a code of length 98 over F4[X]/(X^2) who´s minimum homogenous weight is 278.

Homogenous weight enumerator: w(x)=1x^0+300x^278+315x^280+1164x^282+300x^284+1560x^286+912x^288+2148x^290+540x^292+2112x^294+795x^296+1956x^298+660x^300+1608x^302+381x^304+1020x^306+36x^308+372x^310+66x^312+48x^314+39x^320+15x^328+21x^336+9x^344+6x^352

The gray image is a linear code over GF(4) with n=392, k=7 and d=278.
This code was found by Heurico 1.16 in 12 seconds.