The generator matrix

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

generates a code of length 99 over F4[X]/(X^2) who´s minimum homogenous weight is 278.

Homogenous weight enumerator: w(x)=1x^0+204x^278+432x^279+210x^280+1932x^282+1656x^283+384x^284+3732x^286+2916x^287+558x^288+4740x^290+3288x^291+582x^292+6264x^294+3900x^295+630x^296+6204x^298+4188x^299+489x^300+5832x^302+3576x^303+456x^304+4440x^306+2544x^307+333x^308+2508x^310+1356x^311+228x^312+816x^314+612x^315+102x^316+180x^318+108x^319+54x^320+12x^322+12x^324+21x^328+9x^332+9x^336+9x^340+3x^344+6x^352

The gray image is a linear code over GF(4) with n=396, k=8 and d=278.
This code was found by Heurico 1.16 in 31.2 seconds.