The generator matrix

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

generates a code of length 57 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+270x^49+1506x^50+3430x^51+6903x^52+12606x^53+20630x^54+29196x^55+36833x^56+38894x^57+37167x^58+29854x^59+21073x^60+12100x^61+6495x^62+3164x^63+1248x^64+466x^65+211x^66+50x^67+20x^68+14x^69+7x^70+2x^72+2x^73+2x^75

The gray image is a code over GF(2) with n=456, k=18 and d=196.
This code was found by Heurico 1.16 in 503 seconds.