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

generates a code of length 84 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 236.

Homogenous weight enumerator: w(x)=1x^0+93x^236+147x^240+48x^243+165x^244+432x^247+141x^248+1296x^251+120x^252+1296x^255+117x^256+54x^260+45x^264+36x^268+18x^272+24x^276+9x^280+15x^284+15x^288+9x^292+3x^296+6x^300+3x^308+3x^324

The gray image is a linear code over GF(4) with n=336, k=6 and d=236.
This code was found by Heurico 1.16 in 0.336 seconds.