The generator matrix

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

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+420x^164+444x^165+360x^166+180x^167+1950x^168+1632x^169+1236x^170+648x^171+3639x^172+2400x^173+1524x^174+1068x^175+4860x^176+3552x^177+2628x^178+1248x^179+5967x^180+3948x^181+3072x^182+1788x^183+6198x^184+3408x^185+2412x^186+984x^187+3885x^188+2232x^189+900x^190+228x^191+1482x^192+720x^193+156x^194+168x^196+96x^197+51x^200+21x^204+9x^208+9x^212+9x^216+3x^220

The gray image is a linear code over GF(4) with n=240, k=8 and d=164.
This code was found by Heurico 1.16 in 17.1 seconds.