The generator matrix

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

generates a code of length 57 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 156.

Homogenous weight enumerator: w(x)=1x^0+372x^156+396x^157+420x^158+1200x^159+2136x^160+1296x^161+1140x^162+2184x^163+3720x^164+2292x^165+1452x^166+2904x^167+4773x^168+2688x^169+2052x^170+3780x^171+5601x^172+3192x^173+1920x^174+3708x^175+5181x^176+2388x^177+1440x^178+2220x^179+2946x^180+1272x^181+672x^182+876x^183+807x^184+300x^185+120x^186+24x^187+57x^188+6x^192

The gray image is a linear code over GF(4) with n=228, k=8 and d=156.
This code was found by Heurico 1.16 in 16.3 seconds.