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 a^2*X  X  1  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  1  1 a^2*X+1 a^2*X+1 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^2  1 X+a^2 a^2*X  a
 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  X  X a^2*X a^2*X 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+492x^282+276x^283+42x^284+1224x^285+1452x^286+492x^287+30x^288+1356x^289+1332x^290+480x^291+51x^292+1212x^293+1116x^294+288x^295+54x^296+792x^297+1020x^298+264x^299+30x^300+792x^301+528x^302+228x^303+15x^304+528x^305+420x^306+120x^307+15x^308+456x^309+420x^310+144x^311+12x^312+132x^313+96x^314+12x^315+6x^316+12x^317+36x^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 1.94 seconds.