The generator matrix

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

generates a code of length 59 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 160.

Homogenous weight enumerator: w(x)=1x^0+120x^160+168x^161+180x^162+624x^163+1014x^164+1200x^165+672x^166+2328x^167+2007x^168+1644x^169+1188x^170+2976x^171+3255x^172+2880x^173+1608x^174+4296x^175+4137x^176+3024x^177+2472x^178+4800x^179+4170x^180+3552x^181+2064x^182+4344x^183+3294x^184+1884x^185+804x^186+1776x^187+1143x^188+912x^189+168x^190+360x^191+210x^192+96x^193+60x^194+42x^196+21x^200+12x^204+18x^208+12x^212

The gray image is a linear code over GF(4) with n=236, k=8 and d=160.
This code was found by Heurico 1.16 in 16.7 seconds.