The generator matrix

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

generates a code of length 53 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+285x^44+652x^45+1676x^46+2012x^47+3060x^48+3708x^49+5374x^50+5504x^51+6768x^52+6568x^53+7416x^54+6092x^55+5326x^56+3844x^57+3266x^58+1704x^59+1175x^60+516x^61+342x^62+112x^63+85x^64+8x^65+32x^66+4x^68+6x^70

The gray image is a code over GF(2) with n=212, k=16 and d=88.
This code was found by Heurico 1.13 in 47 seconds.