The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  0  1  1  1  X  1  1  1  1  1  0  1  1  1  1  1  1  1  1  1 (a+1)X  1  1  X  1  X  1 (a+1)X  1  1  1  1 (a+1)X  1  1  X  1  1  X  1  1 aX  1  1  1 aX  1 aX  1  1 (a+1)X  0 (a+1)X  1  1  1  1
 0  1  1  a a+1  0 (a+1)X+1 (a+1)X+a+1  a  1  0 (a+1)X+1 (a+1)X+a+1  1  a  X (a+1)X+a+1  1 (a+1)X+1  a aX+a+1  0 aX+1  1  a (a+1)X+a+1 (a+1)X+a+1 aX+1 aX+a+1 aX X+a  0  1  1 (a+1)X+1 X+1  1 aX  1 (a+1)X+a  1 aX+1 X+a+1 aX+a aX+a+1  1 (a+1)X  X  1 (a+1)X+a+1 (a+1)X+1  1 aX+a aX  1 (a+1)X+a X+1 aX+1  1 aX+a  1 a+1 X+a  1  1  1 a+1 X+a+1  1 X+a+1
 0  0 (a+1)X  0  0  0  X aX  X  X  X (a+1)X (a+1)X aX aX aX  0  0  X aX (a+1)X aX (a+1)X (a+1)X (a+1)X aX aX  X (a+1)X  X aX  X  X aX aX  0 aX aX  X  X aX aX  X aX  X aX aX aX (a+1)X  X aX (a+1)X  X (a+1)X (a+1)X (a+1)X aX  X  0 (a+1)X  X (a+1)X  X  X  X  0  0  X (a+1)X  X
 0  0  0  X  0  X (a+1)X (a+1)X  X (a+1)X  0 (a+1)X  X  X  0  X (a+1)X  0 (a+1)X  0  0  X (a+1)X (a+1)X  X aX (a+1)X (a+1)X (a+1)X  X (a+1)X  0  0  X aX (a+1)X (a+1)X  X  X  X (a+1)X  X aX (a+1)X (a+1)X (a+1)X  0 (a+1)X  X  X  X  0 (a+1)X aX (a+1)X  0  0  0 aX  X  X (a+1)X  X (a+1)X aX aX (a+1)X aX  X  X
 0  0  0  0 (a+1)X (a+1)X (a+1)X (a+1)X  0 aX  X aX  0 aX (a+1)X  X  X (a+1)X  X aX  X (a+1)X  0 (a+1)X aX  X  0  0 (a+1)X  X aX (a+1)X aX (a+1)X (a+1)X aX aX aX  0  X  0  X (a+1)X  0 (a+1)X (a+1)X  0  X aX  X  0 (a+1)X  X  X aX  0  0  X aX  0  X  X (a+1)X  0 aX (a+1)X  0  0 (a+1)X (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+357x^196+252x^197+156x^198+885x^200+672x^201+444x^202+1143x^204+1104x^205+504x^206+1233x^208+1224x^209+696x^210+1332x^212+1452x^213+780x^214+1113x^216+1056x^217+396x^218+768x^220+360x^221+96x^222+189x^224+24x^225+51x^228+24x^232+27x^236+15x^240+15x^244+12x^248+3x^260

The gray image is a linear code over GF(4) with n=280, k=7 and d=196.
This code was found by Heurico 1.16 in 16.7 seconds.