The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  X  1  1 X+2  1  1 X+2  1  0  1  1  1  0  1  2  1  1  1  X  1 X+2  1  1  1  2  1  2  1  1  1  1  1  X  1  1  1 X+2 X+2 X+2  1  1  X X+2  0  1  1  1  2  X  1  1
 0  1  1  0 X+3  1  X X+1  1 X+2  1  3 X+3  1 X+2  1  1  2  1  0  3 X+2  1 X+1  1  0 X+3  3  1 X+2  1  2 X+3  0  1  3  1  0  1  0 X+3 X+1  1 X+3  2  0  1  1  1 X+3 X+3  2  1  2  1 X+1 X+2  0  X  2  0
 0  0  X  0 X+2  0  0  X  2  0  2  X  0 X+2  X  2  X X+2 X+2 X+2  0  X  X  2 X+2  2  X  X  X  0  0  X  X  0  2  X  0 X+2  X  X  0  2 X+2  2  0  2  0  X  X X+2 X+2 X+2 X+2  X  X X+2 X+2  2 X+2  2  0
 0  0  0  X  0  0  X  X X+2  2  X  X  X X+2 X+2  X  2  0  X X+2  0  2  2  0  2  2  X X+2  2  0 X+2  2  X X+2  0  2 X+2 X+2  0 X+2 X+2  0 X+2  X  X X+2  2 X+2 X+2 X+2  0  X  X  X  X  0  0  X  2 X+2  0
 0  0  0  0  2  0  0  0  0  0  0  2  0  2  0  0  2  0  0  2  2  2  0  2  2  2  0  2  0  0  2  2  0  0  2  2  2  2  0  2  0  2  2  2  2  2  2  0  2  2  2  2  2  0  0  0  2  0  0  0  0
 0  0  0  0  0  2  0  0  0  2  0  2  2  0  2  0  2  2  0  2  0  0  0  0  0  0  2  2  2  0  2  2  0  2  2  2  2  2  2  0  0  0  2  0  2  2  0  0  0  0  0  2  2  2  0  0  0  2  2  2  0
 0  0  0  0  0  0  2  0  0  0  2  0  0  0  0  0  2  2  2  2  2  2  2  0  0  2  0  2  0  2  2  2  2  0  0  0  0  0  0  2  2  2  0  2  2  0  0  2  0  0  2  0  2  0  0  2  0  0  2  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+48x^52+92x^53+214x^54+288x^55+576x^56+408x^57+769x^58+498x^59+1001x^60+554x^61+951x^62+522x^63+855x^64+376x^65+384x^66+174x^67+170x^68+88x^69+90x^70+46x^71+32x^72+16x^73+23x^74+8x^75+5x^76+2x^77+1x^78

The gray image is a code over GF(2) with n=244, k=13 and d=104.
This code was found by Heurico 1.16 in 4.08 seconds.