The generator matrix

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

generates a code of length 61 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+249x^52+68x^53+568x^54+368x^55+959x^56+812x^57+1460x^58+1092x^59+1956x^60+1420x^61+1882x^62+1164x^63+1525x^64+820x^65+870x^66+316x^67+402x^68+80x^69+230x^70+4x^71+75x^72+38x^74+16x^76+8x^78+1x^84

The gray image is a code over GF(2) with n=244, k=14 and d=104.
This code was found by Heurico 1.16 in 15.6 seconds.