The generator matrix

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

generates a code of length 54 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+362x^45+724x^46+1558x^47+1950x^48+3054x^49+3822x^50+5344x^51+5576x^52+7148x^53+6538x^54+6878x^55+5794x^56+5542x^57+3762x^58+3206x^59+1746x^60+1344x^61+626x^62+284x^63+159x^64+76x^65+16x^66+10x^67+6x^68+10x^69

The gray image is a code over GF(2) with n=216, k=16 and d=90.
This code was found by Heurico 1.13 in 167 seconds.