The generator matrix

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

generates a code of length 48 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+85x^40+766x^41+2482x^42+5462x^43+11239x^44+19540x^45+29916x^46+39628x^47+43127x^48+40008x^49+31045x^50+19688x^51+10797x^52+5144x^53+2018x^54+726x^55+315x^56+90x^57+39x^58+14x^59+2x^60+4x^61+4x^62+2x^63+2x^64

The gray image is a code over GF(2) with n=384, k=18 and d=160.
This code was found by Heurico 1.16 in 382 seconds.