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

generates a code of length 82 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 232.

Homogenous weight enumerator: w(x)=1x^0+165x^232+201x^236+144x^238+138x^240+720x^242+123x^244+1200x^246+87x^248+1008x^250+57x^252+66x^256+45x^260+27x^264+30x^268+39x^272+12x^276+15x^280+12x^284+3x^296+3x^312

The gray image is a linear code over GF(4) with n=328, k=6 and d=232.
This code was found by Heurico 1.16 in 0.5 seconds.