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

generates a code of length 74 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 216.

Homogenous weight enumerator: w(x)=1x^0+312x^216+2304x^218+192x^220+252x^224+192x^228+72x^232+768x^234+3x^256

The gray image is a linear code over GF(4) with n=296, k=6 and d=216.
This code was found by Heurico 1.16 in 10.7 seconds.