The generator matrix

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

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+780x^275+390x^276+924x^279+264x^280+600x^283+132x^284+300x^287+75x^288+228x^291+60x^292+96x^295+48x^296+60x^299+36x^300+72x^303+12x^304+12x^307+3x^308+3x^340

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 9.44 seconds.