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

generates a code of length 69 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 192.

Homogenous weight enumerator: w(x)=1x^0+84x^192+201x^196+48x^198+156x^200+432x^202+159x^204+1296x^206+114x^208+1296x^210+45x^212+66x^216+57x^220+39x^224+30x^228+18x^232+27x^236+12x^240+6x^244+3x^248+3x^252+3x^264

The gray image is a linear code over GF(4) with n=276, k=6 and d=192.
This code was found by Heurico 1.16 in 0.242 seconds.