The generator matrix

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

generates a code of length 61 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+118x^55+308x^56+410x^57+426x^58+400x^59+354x^60+366x^61+375x^62+308x^63+270x^64+202x^65+153x^66+144x^67+101x^68+74x^69+51x^70+22x^71+5x^72+4x^73+1x^74+1x^76+2x^78

The gray image is a code over GF(2) with n=244, k=12 and d=110.
This code was found by Heurico 1.16 in 0.625 seconds.