The generator matrix

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

generates a code of length 51 over F4[X]/(X^2) who´s minimum homogenous weight is 150.

Homogenous weight enumerator: w(x)=1x^0+120x^150+33x^152+24x^156+72x^158+3x^160+3x^184

The gray image is a linear code over GF(4) with n=204, k=4 and d=150.
This code was found by Heurico 1.16 in 0.015 seconds.