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  0  0  1  1  1  1
 0  X X^2+2 X^2+X  0 X^2+X X^2+2 X+2  0 X^2+X X^2+2 X+2 X^2 X+2  0 X^2+X  2 X^2+X+2 X^2+2 X+2  0 X^2+X  2 X^2+X+2 X^2+2 X^2 X+2 X+2  2 X^2+X X^2  X X^2+2  0  0 X^2+X X^2+X+2 X^2+2  X X^2+2  X  X X^2 X+2 X^2+2 X^2  0
 0  0  2  0  0  0  0  0  0  0  2  2  0  2  2  2  2  2  0  2  2  0  0  0  0  2  0  2  2  2  2  2  0  2  2  0  2  0  2  0  0  0  0  0  2  2  0
 0  0  0  2  0  0  0  0  0  2  2  2  2  2  0  0  0  2  2  0  2  2  2  2  2  0  0  0  2  0  2  2  0  2  0  0  2  0  2  0  0  2  0  2  2  0  2
 0  0  0  0  2  0  0  2  2  2  0  0  0  2  0  2  2  2  0  0  0  2  2  0  2  2  2  2  2  0  2  0  0  0  2  0  0  2  2  0  0  2  2  0  0  0  0
 0  0  0  0  0  2  2  2  2  0  2  0  0  2  2  2  2  0  2  0  0  2  0  2  2  0  0  0  0  2  2  2  0  2  0  0  2  0  0  0  2  0  0  2  0  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+54x^42+88x^43+101x^44+128x^45+530x^46+272x^47+542x^48+64x^49+114x^50+88x^51+55x^52+6x^54+4x^56+1x^88

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 0.14 seconds.