The generator matrix

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

generates a code of length 91 over F4[X]/(X^2) who´s minimum homogenous weight is 256.

Homogenous weight enumerator: w(x)=1x^0+42x^256+48x^257+276x^259+312x^260+636x^261+792x^263+621x^264+912x^265+900x^267+573x^268+1032x^269+996x^271+735x^272+960x^273+1140x^275+750x^276+1032x^277+1152x^279+621x^280+816x^281+636x^283+249x^284+552x^285+228x^287+51x^288+144x^289+24x^291+36x^292+12x^293+24x^296+18x^300+18x^304+18x^308+9x^312+6x^316+3x^320+6x^324+3x^328

The gray image is a linear code over GF(4) with n=364, k=7 and d=256.
This code was found by Heurico 1.16 in 2.17 seconds.