The generator matrix

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

generates a code of length 94 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 264.

Homogenous weight enumerator: w(x)=1x^0+468x^264+528x^265+384x^266+300x^267+1830x^268+1260x^269+1128x^270+636x^271+3150x^272+2304x^273+1524x^274+816x^275+4167x^276+2868x^277+2136x^278+1032x^279+4722x^280+3204x^281+2016x^282+984x^283+4941x^284+2844x^285+2148x^286+1224x^287+4173x^288+2592x^289+1536x^290+624x^291+3015x^292+1692x^293+912x^294+360x^295+1521x^296+852x^297+384x^298+156x^299+495x^300+264x^301+108x^302+12x^303+108x^304+24x^305+12x^306+24x^308+21x^312+18x^316+9x^320+6x^324+3x^336

The gray image is a linear code over GF(4) with n=376, k=8 and d=264.
This code was found by Heurico 1.16 in 31.8 seconds.