The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  0  1  1  1  X  1  1  1  1  1  0  1  1  1  1  1  1  1  1  1 (a+1)X  X  1  1  1  1  1  1 aX  1 aX  1  1  1  1 (a+1)X  1  X  0  1  1  1 aX  1  1  1  1  1  1  X aX  1  1  1  1  1  1  1 (a+1)X  1  1  0  1  1 aX  1  0  1  1  1  1  1  1  1  1  1 aX  1
 0  1  1  a a+1  0 (a+1)X+1 (a+1)X+a+1  a  1  0 (a+1)X+1 (a+1)X+a+1  1  a  X (a+1)X+a+1  1 (a+1)X+1  a aX+a+1  0 aX+1  1  a (a+1)X+a+1 aX+1 (a+1)X+a+1  0 X+a aX+a+1 (a+1)X  1  1  1 (a+1)X+1  a aX+a  X X+1 aX  1 (a+1)X+a  1 a+1 aX+a  0 aX+a+1  1 aX+a  1  1 (a+1)X (a+1)X+a+1 X+a  1 X+1 aX aX+1 (a+1)X a+1 aX  1  1 X+1  0 aX+a (a+1)X+1  X aX X+1  1 a+1 X+a  1 aX+1  0  1 X+a+1  1  X aX aX+a X+1  0 (a+1)X (a+1)X+1 (a+1)X+1 aX  1  0
 0  0 (a+1)X  0  0  0  X aX  X  X  X (a+1)X (a+1)X aX aX aX  0  0  X aX (a+1)X aX (a+1)X (a+1)X (a+1)X aX  X aX  X aX (a+1)X  X  X aX aX aX (a+1)X (a+1)X aX  0 aX  0  X (a+1)X (a+1)X (a+1)X  X  0 (a+1)X  X  0  0  0  X  X (a+1)X  0  X  0 aX  0 aX aX  X aX (a+1)X aX (a+1)X  X (a+1)X  0 aX aX aX (a+1)X aX  0  X  0  0 (a+1)X  0 (a+1)X (a+1)X  0 aX (a+1)X  0  0  0  0
 0  0  0  X  0  X (a+1)X (a+1)X  X (a+1)X  0 (a+1)X  X  X  0  X (a+1)X  0 (a+1)X  0  0  X (a+1)X (a+1)X  X aX (a+1)X (a+1)X  X (a+1)X (a+1)X  0  0  X (a+1)X aX  0  X  X aX  0  X (a+1)X  X aX (a+1)X (a+1)X (a+1)X (a+1)X  X aX (a+1)X aX  X  0  0  0 aX  0 (a+1)X  X aX  0 (a+1)X  0  X (a+1)X (a+1)X  0  0 aX aX  X  X  0 aX (a+1)X aX  0  X  0 aX (a+1)X  0  X aX  X  X  0 (a+1)X (a+1)X
 0  0  0  0 (a+1)X (a+1)X (a+1)X (a+1)X  0 aX  X aX  0 aX (a+1)X  X  X (a+1)X  X aX  X (a+1)X  0 (a+1)X aX  X  0  0  X aX (a+1)X (a+1)X aX (a+1)X aX (a+1)X  0  X aX aX  X aX  X  X  X  X  0 aX  0 aX (a+1)X aX (a+1)X  X  X (a+1)X  X aX aX  X (a+1)X aX  X (a+1)X  0  X  0 (a+1)X  0 (a+1)X  0 aX  0  0  0  0  X (a+1)X  X  0  0  X  0 aX  X (a+1)X  X  0 (a+1)X  0  0

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

Homogenous weight enumerator: w(x)=1x^0+57x^256+132x^257+252x^259+357x^260+660x^261+636x^263+486x^264+840x^265+960x^267+657x^268+948x^269+1092x^271+744x^272+996x^273+1368x^275+744x^276+1020x^277+996x^279+543x^280+816x^281+672x^283+318x^284+492x^285+156x^287+51x^288+192x^289+12x^291+39x^292+48x^293+18x^296+18x^300+21x^304+18x^308+3x^312+9x^316+12x^320

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.