The generator matrix

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

generates a code of length 74 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 208.

Homogenous weight enumerator: w(x)=1x^0+138x^208+189x^212+48x^213+180x^216+432x^217+117x^220+1296x^221+87x^224+1296x^225+90x^228+51x^232+39x^236+36x^240+15x^244+36x^248+18x^252+6x^256+6x^260+9x^264+3x^268+3x^284

The gray image is a linear code over GF(4) with n=296, k=6 and d=208.
This code was found by Heurico 1.16 in 0.271 seconds.