The generator matrix

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

generates a code of length 98 over F4[X]/(X^2) who´s minimum homogenous weight is 276.

Homogenous weight enumerator: w(x)=1x^0+396x^276+732x^277+408x^278+156x^279+1395x^280+2376x^281+912x^282+420x^283+2175x^284+4284x^285+1200x^286+432x^287+2757x^288+5448x^289+1488x^290+456x^291+3039x^292+5508x^293+1308x^294+384x^295+3084x^296+5784x^297+1524x^298+480x^299+2940x^300+4620x^301+1140x^302+432x^303+2058x^304+3192x^305+648x^306+168x^307+990x^308+1440x^309+444x^310+132x^311+366x^312+288x^313+132x^314+12x^315+168x^316+120x^317+12x^318+24x^320+33x^324+15x^328+3x^332+6x^336+6x^344

The gray image is a linear code over GF(4) with n=392, k=8 and d=276.
This code was found by Heurico 1.16 in 33.5 seconds.