The generator matrix

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

generates a code of length 48 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+59x^44+266x^45+171x^46+412x^47+243x^48+400x^49+168x^50+260x^51+56x^52+6x^53+3x^54+2x^58+1x^76

The gray image is a code over GF(2) with n=384, k=11 and d=176.
This code was found by Heurico 1.16 in 0.11 seconds.