The generator matrix

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

generates a code of length 51 over F4[X]/(X^2) who´s minimum homogenous weight is 139.

Homogenous weight enumerator: w(x)=1x^0+120x^139+225x^140+1056x^143+525x^144+1764x^147+729x^148+2688x^151+756x^152+3552x^155+900x^156+2496x^159+672x^160+612x^163+132x^164+45x^168+48x^172+21x^176+21x^180+9x^184+9x^188+3x^192

The gray image is a linear code over GF(4) with n=204, k=7 and d=139.
This code was found by Heurico 1.16 in 1.58 seconds.