The generator matrix

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

generates a code of length 70 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 199.

Homogenous weight enumerator: w(x)=1x^0+1164x^199+507x^200+2232x^203+777x^204+2604x^207+861x^208+2376x^211+864x^212+1692x^215+504x^216+1152x^219+345x^220+780x^223+204x^224+288x^227+30x^228+3x^232

The gray image is a linear code over GF(4) with n=280, k=7 and d=199.
This code was found by Heurico 1.16 in 61.8 seconds.