The generator matrix

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

generates a code of length 59 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 161.

Homogenous weight enumerator: w(x)=1x^0+108x^161+48x^162+96x^163+180x^164+504x^165+228x^166+276x^167+174x^168+1176x^169+408x^170+564x^171+171x^172+1512x^173+648x^174+540x^175+102x^176+2136x^177+624x^178+552x^179+108x^180+2088x^181+708x^182+780x^183+78x^184+1368x^185+360x^186+228x^187+54x^188+312x^189+48x^190+36x^191+36x^192+12x^193+39x^196+33x^200+12x^204+21x^208+9x^212+3x^216+3x^220

The gray image is a linear code over GF(4) with n=236, k=7 and d=161.
This code was found by Heurico 1.16 in 2.62 seconds.