The generator matrix

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

generates a code of length 92 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 257.

Homogenous weight enumerator: w(x)=1x^0+72x^257+444x^258+372x^259+441x^260+516x^261+1944x^262+840x^263+840x^264+1140x^265+3204x^266+1584x^267+1386x^268+1548x^269+4536x^270+1992x^271+1617x^272+2232x^273+5160x^274+1896x^275+1689x^276+2256x^277+5232x^278+1920x^279+1707x^280+2124x^281+4812x^282+1788x^283+1407x^284+1452x^285+3192x^286+1128x^287+816x^288+744x^289+1572x^290+540x^291+207x^292+180x^293+552x^294+168x^295+33x^296+24x^297+72x^298+60x^299+27x^300+24x^304+15x^308+9x^312+9x^316+3x^320+3x^328+3x^332+3x^336

The gray image is a linear code over GF(4) with n=368, k=8 and d=257.
This code was found by Heurico 1.16 in 30.5 seconds.