The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  X  X  1  1  1  X  X  1  1  X  1  2  1  X  X  1  1  X  X  1  1  X  1  2  1  1  X  1  2  2  1
 0  X  0  0  0  0  0  0  0  X X+2  X  X  2  X X+2  2  0 X+2  X X+2  2  2  0 X+2  0 X+2  X  X  2  2  X  X  X  0  0  X  0  X  2  0  X  2  2  2 X+2  X  X  X  0  X  0 X+2  2  0 X+2  X  0  0  2  0
 0  0  X  0  0  0  X X+2  X  X  X  0  X  0  2 X+2  2  X  2  2 X+2  0  0 X+2  0 X+2 X+2  0  X  0  2 X+2 X+2  2  X  X X+2 X+2  2  2  0 X+2  2  X  X  0  0 X+2  2  2  0  X  0  0 X+2 X+2  2  2  0  X  0
 0  0  0  X  0  X  X  X  2  0  0  2  X  2 X+2  X  2  2 X+2  2  X  X X+2  0  0 X+2 X+2 X+2  0  X  X X+2  0 X+2  X X+2  2  X  X X+2  0  X  X  0  X  X  X  0 X+2  2  X  0  2  2 X+2  X  0  0  X  X  0
 0  0  0  0  X  X  2 X+2 X+2  0  X  X  X X+2  2  0  2 X+2  X  0 X+2  X  2  0  X  0  2  X  0 X+2 X+2 X+2  X  0 X+2  2  2  X  2  0 X+2  0  X  0  X  0  0  2 X+2  X X+2  X X+2  X  X  X X+2  0  2  2  0
 0  0  0  0  0  2  2  2  2  2  0  0  0  2  0  0  2  0  2  2  2  0  2  2  2  0  2  0  0  2  0  0  2  2  0  2  2  0  2  0  2  2  0  2  2  0  2  0  0  0  0  0  0  2  0  0  2  2  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+47x^52+68x^53+126x^54+160x^55+194x^56+304x^57+310x^58+318x^59+365x^60+398x^61+395x^62+330x^63+294x^64+250x^65+123x^66+118x^67+92x^68+50x^69+53x^70+30x^71+27x^72+14x^73+10x^74+4x^75+4x^76+4x^77+6x^78+1x^90

The gray image is a code over GF(2) with n=244, k=12 and d=104.
This code was found by Heurico 1.16 in 1.18 seconds.