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

generates a code of length 94 over F4[X]/(X^2) who´s minimum homogenous weight is 256.

Homogenous weight enumerator: w(x)=1x^0+90x^256+288x^260+369x^264+522x^268+696x^272+2046x^276+3918x^280+4686x^284+2505x^288+273x^292+252x^296+207x^300+165x^304+111x^308+75x^312+87x^316+48x^320+30x^324+6x^328+6x^332+3x^352

The gray image is a linear code over GF(4) with n=376, k=7 and d=256.
This code was found by Heurico 1.16 in 4.54 seconds.