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  X  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  1 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  X aX+a+1 X+a aX+a
 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  0 X+a+1 aX+a+1  1

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+456x^162+576x^163+498x^164+708x^165+2172x^166+1968x^167+1338x^168+1368x^169+3432x^170+3264x^171+1590x^172+1836x^173+4752x^174+3852x^175+2049x^176+2532x^177+5124x^178+4344x^179+2226x^180+2484x^181+4668x^182+3696x^183+1647x^184+1320x^185+2880x^186+1896x^187+741x^188+444x^189+984x^190+372x^191+138x^192+60x^193+108x^194+6x^196+3x^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 15.6 seconds.