The generator matrix

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

generates a code of length 57 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 163.

Homogenous weight enumerator: w(x)=1x^0+180x^163+192x^164+348x^165+204x^166+492x^167+465x^168+264x^169+168x^170+228x^171+240x^172+96x^173+108x^174+168x^175+135x^176+72x^177+60x^178+192x^179+105x^180+132x^181+24x^182+36x^183+72x^184+48x^185+12x^186+48x^187+3x^188+3x^192

The gray image is a linear code over GF(4) with n=228, k=6 and d=163.
This code was found by Heurico 1.16 in 0.0659 seconds.