The generator matrix

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

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+200x^55+153x^56+554x^57+239x^58+586x^59+190x^60+608x^61+116x^62+498x^63+148x^64+268x^65+96x^66+230x^67+41x^68+96x^69+24x^70+14x^71+10x^72+10x^73+5x^74+8x^75+1x^76

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 9.71 seconds.