The generator matrix

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

generates a code of length 70 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 198.

Homogenous weight enumerator: w(x)=1x^0+456x^198+600x^199+141x^200+1668x^202+1164x^203+189x^204+1920x^206+1152x^207+234x^208+1656x^210+1116x^211+144x^212+1524x^214+1032x^215+159x^216+1152x^218+660x^219+93x^220+564x^222+288x^223+30x^224+276x^226+132x^227+30x^228+3x^240

The gray image is a linear code over GF(4) with n=280, k=7 and d=198.
This code was found by Heurico 1.16 in 1.03 seconds.