The generator matrix

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

generates a code of length 47 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+138x^42+188x^43+364x^44+440x^45+718x^46+596x^47+647x^48+376x^49+240x^50+140x^51+116x^52+48x^53+70x^54+4x^55+7x^56+2x^58+1x^72

The gray image is a code over GF(2) with n=376, k=12 and d=168.
This code was found by Heurico 1.16 in 0.282 seconds.