The generator matrix

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

generates a code of length 57 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 164.

Homogenous weight enumerator: w(x)=1x^0+408x^164+540x^165+360x^166+456x^168+408x^169+156x^170+429x^172+168x^173+48x^174+243x^176+168x^177+120x^178+144x^180+204x^181+72x^182+108x^184+48x^185+12x^186+3x^188

The gray image is a linear code over GF(4) with n=228, k=6 and d=164.
This code was found by Heurico 1.16 in 23.3 seconds.