The generator matrix

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

generates a code of length 99 over F4[X]/(X^2) who´s minimum homogenous weight is 272.

Homogenous weight enumerator: w(x)=1x^0+141x^272+300x^276+405x^280+60x^283+435x^284+420x^287+384x^288+1560x^291+405x^292+3720x^295+303x^296+4332x^299+315x^300+2196x^303+240x^304+231x^308+204x^312+198x^316+129x^320+135x^324+114x^328+66x^332+42x^336+15x^340+18x^344+6x^348+3x^352+3x^356+3x^372

The gray image is a linear code over GF(4) with n=396, k=7 and d=272.
This code was found by Heurico 1.16 in 4.87 seconds.