The generator matrix

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

generates a code of length 48 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+162x^41+1161x^42+2810x^43+6385x^44+9566x^45+15637x^46+18414x^47+22238x^48+19100x^49+16284x^50+9316x^51+6026x^52+2374x^53+979x^54+430x^55+131x^56+22x^57+17x^58+6x^59+3x^60+8x^61+2x^62

The gray image is a code over GF(2) with n=384, k=17 and d=164.
This code was found by Heurico 1.16 in 96.4 seconds.