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

generates a code of length 47 over F4[X]/(X^2) who´s minimum homogenous weight is 134.

Homogenous weight enumerator: w(x)=1x^0+540x^134+405x^136+1104x^138+264x^140+552x^142+132x^144+432x^146+120x^148+348x^150+96x^152+96x^154+3x^160+3x^168

The gray image is a linear code over GF(4) with n=188, k=6 and d=134.
This code was found by Heurico 1.16 in 0.593 seconds.