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

generates a code of length 76 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 212.

Homogenous weight enumerator: w(x)=1x^0+54x^212+180x^216+48x^219+216x^220+432x^223+111x^224+1296x^227+105x^228+1296x^231+102x^232+66x^236+33x^240+27x^244+36x^248+30x^252+21x^256+15x^260+12x^264+6x^268+6x^276+3x^292

The gray image is a linear code over GF(4) with n=304, k=6 and d=212.
This code was found by Heurico 1.16 in 0.281 seconds.