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

generates a code of length 46 over F4[X]/(X^2) who´s minimum homogenous weight is 131.

Homogenous weight enumerator: w(x)=1x^0+444x^131+312x^132+96x^133+264x^134+600x^135+417x^136+12x^137+168x^138+516x^139+159x^140+24x^141+60x^142+252x^143+204x^144+60x^145+48x^146+192x^147+117x^148+36x^150+108x^151+6x^160

The gray image is a linear code over GF(4) with n=184, k=6 and d=131.
This code was found by Heurico 1.16 in 0.14 seconds.