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

generates a code of length 93 over F4[X]/(X^2) who´s minimum homogenous weight is 256.

Homogenous weight enumerator: w(x)=1x^0+246x^256+342x^260+420x^264+72x^265+429x^268+360x^269+381x^272+1680x^273+360x^276+3600x^277+366x^280+4392x^281+285x^284+2184x^285+249x^288+243x^292+189x^296+183x^300+111x^304+102x^308+75x^312+48x^316+33x^320+21x^324+6x^328+3x^336+3x^348

The gray image is a linear code over GF(4) with n=372, k=7 and d=256.
This code was found by Heurico 1.16 in 47 seconds.