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

generates a code of length 97 over F4[X]/(X^2) who´s minimum homogenous weight is 264.

Homogenous weight enumerator: w(x)=1x^0+57x^264+198x^268+393x^272+399x^276+48x^279+441x^280+576x^283+366x^284+2592x^287+315x^288+5184x^291+378x^292+3888x^295+261x^296+204x^300+252x^304+204x^308+180x^312+150x^316+117x^320+66x^324+45x^328+30x^332+18x^336+18x^340+3x^372

The gray image is a linear code over GF(4) with n=388, k=7 and d=264.
This code was found by Heurico 1.16 in 4.7 seconds.