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

generates a code of length 94 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 265.

Homogenous weight enumerator: w(x)=1x^0+396x^265+648x^266+540x^267+1209x^268+1776x^269+1452x^270+1092x^271+2274x^272+2880x^273+2292x^274+1356x^275+2562x^276+3240x^277+2664x^278+1476x^279+3012x^280+3228x^281+2796x^282+1296x^283+3030x^284+3528x^285+2760x^286+1272x^287+2574x^288+3132x^289+2304x^290+996x^291+1938x^292+2160x^293+1296x^294+732x^295+930x^296+864x^297+492x^298+420x^299+321x^300+240x^301+180x^302+36x^303+33x^304+60x^305+12x^306+36x^308

The gray image is a linear code over GF(4) with n=376, k=8 and d=265.
This code was found by Heurico 1.16 in 28.6 seconds.