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

generates a code of length 52 over F4[X]/(X^2) who´s minimum homogenous weight is 149.

Homogenous weight enumerator: w(x)=1x^0+420x^149+504x^150+192x^151+24x^152+480x^153+552x^154+168x^155+18x^156+336x^157+264x^158+108x^159+168x^161+216x^162+96x^163+9x^164+252x^165+96x^166+12x^167+3x^168+72x^169+96x^170+9x^172

The gray image is a linear code over GF(4) with n=208, k=6 and d=149.
This code was found by Heurico 1.16 in 1.67 seconds.