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

generates a code of length 60 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 164.

Homogenous weight enumerator: w(x)=1x^0+45x^164+162x^168+210x^172+192x^174+141x^176+1152x^178+123x^180+1728x^182+72x^184+57x^188+60x^192+42x^196+27x^200+36x^204+24x^208+12x^212+6x^216+3x^220+3x^232

The gray image is a linear code over GF(4) with n=240, k=6 and d=164.
This code was found by Heurico 1.16 in 0.195 seconds.