The generator matrix

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

generates a code of length 93 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 262.

Homogenous weight enumerator: w(x)=1x^0+420x^262+516x^263+576x^264+792x^265+1776x^266+1788x^267+1218x^268+1656x^269+3192x^270+2844x^271+1746x^272+1800x^273+3492x^274+2532x^275+1887x^276+1980x^277+3816x^278+3144x^279+2070x^280+2076x^281+3480x^282+2832x^283+1881x^284+1704x^285+3180x^286+2496x^287+1224x^288+1248x^289+2280x^290+1500x^291+705x^292+780x^293+1104x^294+588x^295+348x^296+228x^297+252x^298+180x^299+93x^300+24x^301+48x^302+12x^303+27x^304

The gray image is a linear code over GF(4) with n=372, k=8 and d=262.
This code was found by Heurico 1.16 in 27.9 seconds.