The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  1  1 a^2*X  1  1  0 a*X  1  1  1 a^2*X  X  1  1  1  1 a^2*X  X  1  1  1  1  1  1  1  1  1 a*X a*X  1  1  1  X  1  1 a*X  1  1  0
 0  1  0  0  X a^2*X  1 a^2*X+a  1 a^2*X+1 a^2*X+1 a^2 a*X+a  a a^2*X+a^2  1 a*X+a^2  a  1  1 a^2 a^2*X+a^2 a*X+1 a^2*X  1  X a*X+a^2 a^2*X+a  a  1  0 a*X+a  1 a*X+a a^2 a^2*X a*X+a X+a^2  0 X+a^2  1  1  a X+a^2  X  1 a*X a^2*X+1  1 a^2*X+a^2  0  1
 0  0  1  1 a^2*X+a a^2 X+1 a^2*X+1 a^2  a  X a^2*X+a^2 a^2*X+a^2 X+a X+a a*X+1 a^2*X  X X+a a^2*X+a^2 X+1 a^2*X a^2*X+1  1 a*X a^2 X+1  1 a^2*X+a a^2  1 a*X+1  a X+a^2 a*X+1  a  X a*X+a  0 X+a^2  1 a^2*X+1 a^2*X+a^2 a*X+a a^2*X+a a^2*X+a X+a^2 a*X  a a*X+a  a a^2
 0  0  0 a^2*X  0  0 a^2*X a^2*X a*X a*X  0  0 a^2*X  0 a*X a^2*X a*X a*X  X a^2*X  X a^2*X a*X a*X a^2*X a^2*X  0 a*X a^2*X  X  X  X  X  0 a*X a^2*X a^2*X  0  X a*X  0 a*X a*X a^2*X  X  0  X  X a^2*X  X a^2*X a*X

generates a code of length 52 over F4[X]/(X^2) who´s minimum homogenous weight is 145.

Homogenous weight enumerator: w(x)=1x^0+396x^145+708x^146+228x^147+54x^148+1224x^149+1344x^150+624x^151+75x^152+1524x^153+1476x^154+456x^155+45x^156+1608x^157+1500x^158+528x^159+15x^160+1164x^161+1080x^162+276x^163+30x^164+720x^165+660x^166+192x^167+15x^168+276x^169+144x^170+9x^172+6x^176+6x^180

The gray image is a linear code over GF(4) with n=208, k=7 and d=145.
This code was found by Heurico 1.16 in 12.3 seconds.