The generator matrix

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

generates a code of length 64 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+69x^168+270x^172+432x^176+771x^180+1323x^184+3117x^188+4170x^192+3618x^196+1608x^200+270x^204+249x^208+195x^212+120x^216+99x^220+60x^224+12x^228

The gray image is a linear code over GF(4) with n=256, k=7 and d=168.
This code was found by Heurico 1.16 in 2.88 seconds.