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

generates a code of length 60 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 156.

Homogenous weight enumerator: w(x)=1x^0+30x^156+261x^160+381x^164+426x^168+192x^169+462x^172+1152x^173+363x^176+3072x^177+414x^180+4992x^181+399x^184+2880x^185+369x^188+279x^192+318x^196+165x^200+105x^204+84x^208+27x^212+6x^216+6x^220

The gray image is a linear code over GF(4) with n=240, k=7 and d=156.
This code was found by Heurico 1.16 in 2.65 seconds.