The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  1  1  1  1  1  1  1  1  X  X X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  X  X  X  2  2  1
 0 X^2+2  0 X^2+2  2 X^2  2 X^2  0 X^2+2  0 X^2+2  2 X^2  2 X^2 X^2+2 X^2+2 X^2 X^2  0  2  0  2 X^2+2 X^2  0  2 X^2+2 X^2  0  2 X^2+2 X^2 X^2+2 X^2  0  2 X^2 X^2  2  0  2  0 X^2 X^2  0
 0  0  2  2  2  2  0  0  0  0  2  2  2  2  0  0  0  2  2  0  2  2  0  0  0  0  2  2  2  2  0  0  0  2  2  0  2  2  2  0  0  2  2  0  2  0  0

generates a code of length 47 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+28x^46+70x^47+7x^48+8x^49+12x^50+2x^55

The gray image is a code over GF(2) with n=376, k=7 and d=184.
This code was found by Heurico 1.16 in 0.062 seconds.