The generator matrix

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

generates a code of length 70 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 202.

Homogenous weight enumerator: w(x)=1x^0+264x^202+345x^204+1620x^206+201x^208+288x^210+174x^212+180x^214+219x^216+228x^218+57x^220+456x^222+21x^224+36x^226+3x^232+3x^240

The gray image is a linear code over GF(4) with n=280, k=6 and d=202.
This code was found by Heurico 1.16 in 2.23 seconds.