The generator matrix

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

generates a code of length 47 over F4[X]/(X^2) who´s minimum homogenous weight is 136.

Homogenous weight enumerator: w(x)=1x^0+63x^136+360x^138+90x^140+324x^142+60x^144+30x^148+84x^150+9x^152+3x^160

The gray image is a linear code over GF(4) with n=188, k=5 and d=136.
This code was found by Heurico 1.16 in 0.015 seconds.