The generator matrix

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

generates a code of length 94 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 275.

Homogenous weight enumerator: w(x)=1x^0+528x^275+57x^276+1728x^278+324x^279+81x^280+288x^283+54x^284+60x^287+39x^288+156x^291+9x^292+576x^294+120x^295+6x^296+36x^299+24x^303+9x^312

The gray image is a linear code over GF(4) with n=376, k=6 and d=275.
This code was found by Heurico 1.16 in 61.7 seconds.