The generator matrix

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

generates a code of length 56 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 152.

Homogenous weight enumerator: w(x)=1x^0+63x^152+141x^156+48x^159+165x^160+432x^163+201x^164+1296x^167+102x^168+1296x^171+87x^172+63x^176+39x^180+39x^184+42x^188+45x^192+15x^196+18x^200+3x^212

The gray image is a linear code over GF(4) with n=224, k=6 and d=152.
This code was found by Heurico 1.16 in 0.176 seconds.