The generator matrix

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

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+124x^42+161x^44+64x^45+496x^46+384x^47+500x^48+64x^49+160x^50+30x^52+48x^54+10x^56+4x^58+1x^60+1x^80

The gray image is a code over GF(2) with n=376, k=11 and d=168.
This code was found by Heurico 1.16 in 68.1 seconds.