The generator matrix

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

generates a code of length 53 over F4[X]/(X^2) who´s minimum homogenous weight is 152.

Homogenous weight enumerator: w(x)=1x^0+261x^152+672x^153+192x^154+72x^155+381x^156+600x^157+228x^158+84x^159+231x^160+312x^161+60x^162+156x^164+216x^165+36x^166+36x^167+84x^168+264x^169+36x^170+96x^172+48x^173+24x^174+3x^176+3x^180

The gray image is a linear code over GF(4) with n=212, k=6 and d=152.
This code was found by Heurico 1.16 in 0.109 seconds.