The generator matrix

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

generates a code of length 46 over F4[X]/(X^2) who´s minimum homogenous weight is 134.

Homogenous weight enumerator: w(x)=1x^0+240x^134+186x^136+372x^138+84x^142+60x^144+60x^146+12x^150+6x^152+3x^160

The gray image is a linear code over GF(4) with n=184, k=5 and d=134.
This code was found by Heurico 1.16 in 1.78 seconds.