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

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+786x^152+1566x^156+2880x^160+3666x^164+3891x^168+2622x^172+804x^176+60x^180+33x^184+30x^188+12x^192+18x^196+6x^200+6x^204+3x^208

The gray image is a linear code over GF(4) with n=220, k=7 and d=152.
This code was found by Heurico 1.16 in 41.7 seconds.