The generator matrix

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

generates a code of length 52 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+142x^45+317x^46+384x^47+620x^48+694x^49+777x^50+874x^51+801x^52+814x^53+687x^54+692x^55+538x^56+314x^57+245x^58+140x^59+74x^60+20x^61+20x^62+20x^63+13x^64+2x^66+2x^67+1x^68

The gray image is a code over GF(2) with n=208, k=13 and d=90.
This code was found by Heurico 1.16 in 2.78 seconds.