The generator matrix

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

generates a code of length 53 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+346x^45+652x^46+1244x^47+1635x^48+2240x^49+2374x^50+3046x^51+3047x^52+3458x^53+3007x^54+3448x^55+2591x^56+2194x^57+1351x^58+1030x^59+499x^60+324x^61+161x^62+58x^63+33x^64+14x^65+7x^66+4x^67+2x^68+2x^71

The gray image is a code over GF(2) with n=212, k=15 and d=90.
This code was found by Heurico 1.13 in 351 seconds.