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

generates a code of length 52 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 136.

Homogenous weight enumerator: w(x)=1x^0+216x^136+393x^140+12x^141+393x^144+180x^145+480x^148+1080x^149+411x^152+3240x^153+453x^156+4860x^157+414x^160+2916x^161+396x^164+318x^168+267x^172+189x^176+108x^180+39x^184+15x^188+3x^192

The gray image is a linear code over GF(4) with n=208, k=7 and d=136.
This code was found by Heurico 1.16 in 34.8 seconds.