The generator matrix

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

generates a code of length 70 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 194.

Homogenous weight enumerator: w(x)=1x^0+420x^194+264x^195+342x^196+1320x^197+1788x^198+936x^199+1275x^200+2472x^201+3324x^202+1752x^203+1581x^204+3432x^205+4260x^206+1848x^207+1920x^208+3672x^209+4668x^210+2112x^211+1887x^212+3660x^213+4836x^214+1848x^215+1806x^216+3156x^217+3240x^218+1404x^219+930x^220+1692x^221+1536x^222+492x^223+459x^224+540x^225+492x^226+84x^227+33x^228+24x^229+12x^230+12x^231+3x^232+3x^236

The gray image is a linear code over GF(4) with n=280, k=8 and d=194.
This code was found by Heurico 1.16 in 21.5 seconds.