The generator matrix

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

generates a code of length 57 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 160.

Homogenous weight enumerator: w(x)=1x^0+504x^160+660x^161+528x^162+1257x^164+1140x^165+564x^166+1659x^168+1488x^169+696x^170+1320x^172+1104x^173+552x^174+1281x^176+1020x^177+432x^178+840x^180+540x^181+228x^182+261x^184+192x^185+72x^186+36x^188+6x^192+3x^196

The gray image is a linear code over GF(4) with n=228, k=7 and d=160.
This code was found by Heurico 1.16 in 1.02 seconds.