The generator matrix

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

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+104x^55+307x^56+348x^57+513x^58+390x^59+450x^60+280x^61+411x^62+282x^63+237x^64+188x^65+201x^66+100x^67+122x^68+64x^69+41x^70+34x^71+19x^72+2x^74+2x^75

The gray image is a code over GF(2) with n=244, k=12 and d=110.
This code was found by Heurico 1.11 in 0.326 seconds.