The generator matrix

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

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+198x^156+36x^157+120x^158+663x^160+648x^161+276x^162+1116x^164+732x^165+480x^166+1269x^168+1344x^169+744x^170+1452x^172+1836x^173+888x^174+1197x^176+1272x^177+420x^178+864x^180+276x^181+144x^182+234x^184+87x^188+33x^192+21x^196+18x^200+3x^204+6x^208+3x^212+3x^216

The gray image is a linear code over GF(4) with n=228, k=7 and d=156.
This code was found by Heurico 1.16 in 1.26 seconds.