The generator matrix

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

generates a code of length 59 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 162.

Homogenous weight enumerator: w(x)=1x^0+408x^162+852x^163+504x^164+480x^165+2076x^166+2064x^167+999x^168+1248x^169+4044x^170+3384x^171+1326x^172+1800x^173+4920x^174+3864x^175+1908x^176+1992x^177+5592x^178+4896x^179+1737x^180+2124x^181+4884x^182+3948x^183+1473x^184+1164x^185+3156x^186+2004x^187+675x^188+348x^189+984x^190+444x^191+69x^192+60x^193+48x^194+48x^195+3x^196+6x^200+3x^204

The gray image is a linear code over GF(4) with n=236, k=8 and d=162.
This code was found by Heurico 1.16 in 17.5 seconds.