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  X  1  1  1  1  1  1  1  1  1  X  1  X  1  X  1  1  X  X  X
 0  2  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  0  0  2  2  2  2  0  0  0  0  2  2  2  0  0
 0  0  2  0  0  0  0  0  2  2  2  2  2  2  2  0  0  0  0  0  2  2  2  2  2  0  0  0  2  0  0  0  0  0  0  2  0  2  0  2  0  2  0  2  2  2  0
 0  0  0  2  0  0  0  0  2  0  0  2  0  2  2  2  0  0  2  2  2  2  2  2  2  2  2  2  2  2  2  0  2  2  0  2  2  2  0  0  0  0  0  0  0  0  0
 0  0  0  0  2  0  0  0  2  0  2  2  0  2  0  2  2  2  0  0  0  0  0  0  2  2  0  2  2  0  2  0  2  2  2  0  0  2  2  2  0  2  0  0  0  0  2
 0  0  0  0  0  2  0  0  2  0  2  0  2  0  2  2  2  0  2  0  0  0  0  2  0  2  0  2  2  0  0  2  2  0  2  2  0  0  0  0  2  2  2  2  0  0  2
 0  0  0  0  0  0  2  0  2  2  0  0  2  2  0  2  0  2  2  0  0  0  2  2  2  2  0  2  0  2  0  0  0  2  0  0  0  2  0  0  2  2  2  0  0  2  0
 0  0  0  0  0  0  0  2  2  2  0  2  2  0  0  2  2  0  0  2  0  2  2  0  2  2  2  0  2  0  2  2  0  0  2  2  0  0  2  0  0  0  2  0  0  0  2

generates a code of length 47 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+42x^40+86x^42+40x^44+60x^46+1536x^47+137x^48+88x^50+8x^52+4x^54+26x^56+18x^58+1x^64+1x^80

The gray image is a code over GF(2) with n=376, k=11 and d=160.
This code was found by Heurico 1.16 in 0.141 seconds.