The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  0  1  1  1  X  1  1  0  1  1  1  1  1 aX  1  1  1  1  1  1  1 (a+1)X  1 (a+1)X  1  1  0  1  1  1  1  X  1  1  1  1  1 aX  1  1  1  1  1  1  1  1  1
 0  1  1  a a+1  0 (a+1)X+1 (a+1)X+a+1  a  1  0 (a+1)X+1 (a+1)X+a+1  1  a  X (a+1)X+a+1  1 (a+1)X+1  a  1  0 X+a (a+1)X+a+1 aX+1 X+a  1  X aX+a+1 X+1 X+a (a+1)X+1 (a+1)X+a+1 (a+1)X+a  1 X+a  1 aX+1 (a+1)X+1  1 X+1  0  1 (a+1)X+1  1  X aX+a+1 X+1 (a+1)X+a+1 X+1  1 (a+1)X aX+a+1 X+a  0 a+1  X  1  a  0
 0  0 (a+1)X  0  0  0  X aX  X  X  X (a+1)X (a+1)X aX aX aX  0  0 aX aX (a+1)X (a+1)X aX aX  0 aX aX aX  X (a+1)X (a+1)X (a+1)X (a+1)X (a+1)X  X  X (a+1)X  X  X (a+1)X  0 (a+1)X aX (a+1)X  X  X (a+1)X  X aX  X aX (a+1)X aX  0  0 aX aX (a+1)X aX  0
 0  0  0  X  0  X (a+1)X (a+1)X  X (a+1)X  0 (a+1)X  X  X  0  X (a+1)X  0 aX  X  X (a+1)X (a+1)X (a+1)X (a+1)X  0 (a+1)X  X  X  0 aX (a+1)X aX  0  0  X (a+1)X (a+1)X aX  X aX  X aX  X (a+1)X aX aX  0 aX aX  0  0  0 aX (a+1)X aX  0 (a+1)X  X  0
 0  0  0  0 (a+1)X (a+1)X (a+1)X (a+1)X  0 aX  X aX  0 aX (a+1)X  X  X (a+1)X (a+1)X aX  X (a+1)X  X  0  0  X  X (a+1)X  X (a+1)X  X  X  0  0 aX (a+1)X aX  0  0 (a+1)X  X  0  0  X  X  X (a+1)X (a+1)X (a+1)X (a+1)X aX  X  0  X (a+1)X  0  0 (a+1)X (a+1)X  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+126x^164+456x^167+345x^168+1308x^171+495x^172+2064x^175+675x^176+2604x^179+834x^180+3240x^183+708x^184+2004x^187+615x^188+576x^191+156x^192+36x^195+45x^196+27x^200+18x^204+18x^208+18x^212+6x^216+6x^220+3x^228

The gray image is a linear code over GF(4) with n=240, k=7 and d=164.
This code was found by Heurico 1.16 in 1.33 seconds.