The generator matrix

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

generates a code of length 98 over F4[X]/(X^2) who´s minimum homogenous weight is 281.

Homogenous weight enumerator: w(x)=1x^0+384x^281+288x^282+516x^283+159x^284+1392x^285+552x^286+1080x^287+180x^288+1536x^289+708x^290+840x^291+240x^292+1284x^293+420x^294+636x^295+120x^296+924x^297+348x^298+564x^299+153x^300+876x^301+312x^302+420x^303+81x^304+696x^305+168x^306+276x^307+54x^308+372x^309+192x^310+216x^311+18x^312+180x^313+72x^314+60x^315+18x^316+12x^317+12x^318+24x^321

The gray image is a linear code over GF(4) with n=392, k=7 and d=281.
This code was found by Heurico 1.16 in 1.56 seconds.