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

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+36x^264+312x^267+369x^268+1488x^271+495x^272+1680x^275+621x^276+1992x^279+525x^280+2268x^283+687x^284+2184x^287+687x^288+1464x^291+366x^292+744x^295+132x^296+132x^299+66x^300+24x^303+24x^304+27x^308+12x^312+12x^316+12x^320+6x^324+9x^328+3x^336+6x^340

The gray image is a linear code over GF(4) with n=376, k=7 and d=264.
This code was found by Heurico 1.16 in 2.26 seconds.