The generator matrix

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

generates a code of length 51 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+258x^44+1290x^45+3320x^46+6046x^47+10718x^48+14622x^49+19489x^50+19406x^51+19517x^52+15176x^53+10942x^54+5652x^55+2919x^56+1120x^57+338x^58+152x^59+57x^60+14x^61+22x^62+6x^63+2x^64+2x^65+1x^66+2x^67

The gray image is a code over GF(2) with n=408, k=17 and d=176.
This code was found by Heurico 1.16 in 103 seconds.