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

generates a code of length 55 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 152.

Homogenous weight enumerator: w(x)=1x^0+183x^152+189x^156+192x^159+135x^160+1152x^163+117x^164+1728x^167+102x^168+87x^172+54x^176+36x^180+33x^184+36x^188+30x^192+12x^196+6x^200+3x^212

The gray image is a linear code over GF(4) with n=220, k=6 and d=152.
This code was found by Heurico 1.16 in 0.204 seconds.