The generator matrix

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

generates a code of length 74 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 211.

Homogenous weight enumerator: w(x)=1x^0+984x^211+648x^212+2580x^215+783x^216+2580x^219+852x^220+2172x^223+558x^224+1656x^227+555x^228+1260x^231+408x^232+804x^235+186x^236+228x^239+87x^240+24x^243+15x^244+3x^248

The gray image is a linear code over GF(4) with n=296, k=7 and d=211.
This code was found by Heurico 1.16 in 46.6 seconds.