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

generates a code of length 70 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 196.

Homogenous weight enumerator: w(x)=1x^0+147x^196+174x^200+192x^204+768x^207+129x^208+2304x^211+69x^212+84x^216+39x^220+48x^224+27x^228+30x^232+39x^236+24x^240+12x^244+6x^248+3x^276

The gray image is a linear code over GF(4) with n=280, k=6 and d=196.
This code was found by Heurico 1.16 in 0.405 seconds.