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 X^2  1  1  1  1  1  1  1  1  1  1  1  1  X  1
 0 X^2+2  0 X^2+2  0 X^2+2  2 X^2  0 X^2+2  0 X^2+2  0 X^2  2 X^2+2 X^2+2  2  2 X^2 X^2+2 X^2  0  0  0  0  2  2 X^2+2 X^2+2 X^2 X^2  2  0  0  2  2 X^2+2 X^2+2 X^2 X^2  0  0  2  2  0 X^2+2
 0  0  2  0  0  0  2  0  0  0  0  2  2  2  2  0  0  2  0  0  2  2  0  2  0  2  2  0  2  2  2  2  0  0  0  0  0  0  0  0  0  2  2  2  2  0  2
 0  0  0  2  0  0  0  2  0  0  2  2  2  0  2  2  2  0  2  0  2  0  0  0  2  2  2  2  2  0  0  2  0  2  2  2  2  0  2  2  0  2  0  2  0  2  2
 0  0  0  0  2  0  2  0  0  2  0  0  2  2  0  2  2  0  2  2  0  2  2  2  2  2  0  0  2  0  0  2  0  2  0  0  2  2  0  0  2  0  0  2  2  0  0
 0  0  0  0  0  2  0  2  2  2  2  2  0  0  2  0  2  2  0  0  0  2  2  2  2  2  0  0  2  2  0  0  0  0  0  2  2  0  2  0  2  0  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+17x^42+4x^43+32x^44+48x^45+146x^46+560x^47+147x^48+8x^49+18x^50+12x^51+12x^52+8x^53+10x^54+1x^90

The gray image is a code over GF(2) with n=376, k=10 and d=168.
This code was found by Heurico 1.16 in 0.109 seconds.