The generator matrix

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

generates a code of length 74 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 206.

Homogenous weight enumerator: w(x)=1x^0+540x^206+420x^207+567x^208+636x^209+2220x^210+1272x^211+1737x^212+1392x^213+3468x^214+2196x^215+2541x^216+1824x^217+4344x^218+2340x^219+2640x^220+1956x^221+4752x^222+2592x^223+2541x^224+2232x^225+4668x^226+2292x^227+2679x^228+1476x^229+3600x^230+1800x^231+1389x^232+924x^233+1956x^234+768x^235+654x^236+312x^237+456x^238+144x^239+81x^240+108x^242+18x^244

The gray image is a linear code over GF(4) with n=296, k=8 and d=206.
This code was found by Heurico 1.16 in 22.9 seconds.