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  1 a*X  1  1  1  1  1 a^2*X  0  0  1
 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 a*X+a  1  a a*X+a^2 a*X  0 a^2*X  1  1  1 a*X+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 a^2*X+1 a^2*X+a^2 a*X+a X+a^2 a*X+1 X+1 a*X+1 a^2*X+a^2 a^2*X+a^2 X+1
 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  0 a*X a*X a^2*X  X a^2*X  0  X  0 a^2*X  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+372x^145+720x^146+240x^147+66x^148+1272x^149+1260x^150+612x^151+66x^152+1620x^153+1572x^154+468x^155+39x^156+1308x^157+1548x^158+444x^159+15x^160+1368x^161+972x^162+396x^163+24x^164+732x^165+696x^166+144x^167+21x^168+240x^169+144x^170+15x^172+6x^176+3x^184

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 29.4 seconds.