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

generates a code of length 83 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 232.

Homogenous weight enumerator: w(x)=1x^0+42x^232+168x^236+36x^238+195x^240+288x^242+132x^244+840x^246+99x^248+1152x^250+90x^252+756x^254+84x^256+48x^260+42x^264+27x^268+12x^272+33x^276+12x^280+18x^284+6x^288+9x^292+3x^300+3x^312

The gray image is a linear code over GF(4) with n=332, k=6 and d=232.
This code was found by Heurico 1.16 in 0.327 seconds.