The generator matrix

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

generates a code of length 53 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 148.

Homogenous weight enumerator: w(x)=1x^0+411x^148+612x^149+360x^150+1293x^152+1140x^153+816x^154+1593x^156+1416x^157+804x^158+1560x^160+1272x^161+336x^162+1305x^164+1092x^165+336x^166+678x^168+468x^169+384x^170+315x^172+144x^173+36x^174+9x^176+3x^184

The gray image is a linear code over GF(4) with n=212, k=7 and d=148.
This code was found by Heurico 1.16 in 0.925 seconds.