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  X  X  X  1  1  2  0  2  1  1  1  X  1  1  0  0  0  1  0  1  1  X  X  X  1  1  1  1  2  X  1  1
 0  X  0  0  0  X X+2  X  0  2  2  0  X X+2  X X+2 X+2  0 X+2 X+2 X+2  2  0  0  0  X X+2 X+2  2  2 X+2  0  2 X+2  X  0  X  X X+2  2 X+2  0  2  0  2  X  2  0  2  2  X X+2  X X+2 X+2  2  0  2  2  2  0
 0  0  X  0  X  X X+2  0  0  0 X+2 X+2  X  X  2  0  X  0  2  0 X+2 X+2  2 X+2  2  X  2  2  X  X  X X+2  2  2 X+2  0 X+2  X  0  X  2  X  2  0  X X+2  2  X  X  2  X  0  X  0  0  0 X+2  0  0  X  0
 0  0  0  X  X  0 X+2  X  2 X+2  X  2  2  X  X  2  0  2 X+2  0  X X+2  X  2  X  0 X+2 X+2  X  2  X  0  2  0  0  X  0  X  2 X+2 X+2  X  X  X  0 X+2  0  2  2  0  0 X+2  X  X X+2 X+2  2  X  X  0  0
 0  0  0  0  2  0  0  0  2  0  0  0  0  0  0  2  2  2  2  2  0  0  2  2  2  2  0  0  0  2  2  2  0  0  0  0  0  0  2  2  2  2  2  2  0  2  2  2  0  0  2  0  2  0  2  0  2  0  2  2  0
 0  0  0  0  0  2  0  2  0  0  2  2  0  2  2  0  0  2  0  2  0  0  0  2  2  0  0  0  0  2  2  2  2  2  2  0  0  0  0  2  2  0  0  2  2  0  2  0  2  0  2  0  0  0  2  2  0  2  2  0  0
 0  0  0  0  0  0  2  2  2  2  0  0  2  0  0  0  0  2  0  2  0  0  0  2  2  2  0  2  2  2  2  0  2  0  2  2  2  2  2  0  0  2  2  2  2  2  0  0  2  2  0  0  0  2  2  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+60x^52+60x^53+114x^54+172x^55+161x^56+278x^57+351x^58+362x^59+364x^60+386x^61+382x^62+332x^63+316x^64+234x^65+109x^66+114x^67+75x^68+50x^69+59x^70+38x^71+38x^72+16x^73+7x^74+4x^75+9x^76+1x^78+2x^79+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 1.2 seconds.