The generator matrix

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

generates a code of length 56 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 157.

Homogenous weight enumerator: w(x)=1x^0+384x^157+936x^158+267x^160+1092x^161+1812x^162+135x^164+1428x^165+2148x^166+279x^168+1224x^169+1836x^170+150x^172+1032x^173+1284x^174+102x^176+756x^177+912x^178+18x^180+228x^181+288x^182+63x^184+6x^188+3x^196

The gray image is a linear code over GF(4) with n=224, k=7 and d=157.
This code was found by Heurico 1.16 in 78.8 seconds.