The generator matrix

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

generates a code of length 57 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 155.

Homogenous weight enumerator: w(x)=1x^0+204x^155+492x^156+564x^157+168x^158+1500x^159+1845x^160+1356x^161+324x^162+2544x^163+3438x^164+2388x^165+612x^166+3648x^167+5019x^168+2892x^169+540x^170+4680x^171+6114x^172+3708x^173+624x^174+5052x^175+5247x^176+2820x^177+540x^178+2736x^179+2886x^180+1404x^181+228x^182+1032x^183+417x^184+228x^185+36x^186+108x^187+42x^188+42x^192+27x^196+18x^200+6x^204+3x^208+3x^212

The gray image is a linear code over GF(4) with n=228, k=8 and d=155.
This code was found by Heurico 1.16 in 18.9 seconds.