The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  1  0  1  1 X^2+X  1  1 X^2+2  1  1 X^2+X X+2  1  1  0  1  1  1  1  1  1  1  X X^2+2  1  1  0 X+2  1  1  1  0  2  1  1  1
 0  1 X+1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1  3 X+2  1  0 X+1  1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1 X+2  3  1  1 X+1 X^2+1  1 X^2+X X^2+X+3  0  3  3 X+1  3 X^2+2  1 X^2+2  1  1  1 X^2+X  1 X^2+X+2  1  1 X^2+X+3 X^2+1  0
 0  0  2  0  0  0  0  0  2  2  0  2  2  2  0  2  2  0  0  0  0  2  2  2  2  0  0  0  2  2  0  0  2  2  2  2  2  2  0  2  2  2  2  2  2  2  2  0  0
 0  0  0  2  0  0  2  0  2  2  2  0  2  2  0  0  0  2  0  2  2  0  2  2  0  2  2  2  2  0  0  2  0  2  2  2  0  0  0  0  2  2  2  2  2  0  0  2  0
 0  0  0  0  2  0  2  2  0  0  2  0  0  2  2  0  2  2  0  2  0  2  0  2  2  0  0  2  2  2  2  2  0  2  2  2  2  2  2  2  0  0  2  0  0  0  0  2  0
 0  0  0  0  0  2  0  2  2  0  2  2  0  2  0  2  0  2  2  2  2  2  2  2  0  2  0  0  2  2  2  2  0  0  2  0  0  2  2  2  2  2  0  0  0  2  2  2  2

generates a code of length 49 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+57x^44+240x^45+314x^46+516x^47+592x^48+664x^49+599x^50+544x^51+301x^52+184x^53+41x^54+28x^55+6x^56+3x^58+1x^60+1x^62+1x^64+2x^66+1x^68

The gray image is a code over GF(2) with n=392, k=12 and d=176.
This code was found by Heurico 1.16 in 0.218 seconds.