The generator matrix

 1  0  0  1  1  1  0  1  1  2  1  2  1  2  X  1 X+2  1  1  1  1 X+2  1  2 X+2  X  1  1  1  1  1  1 X+2  2  1  X  0  0  1  1  X  1  X  1 X+2  1  X  1  1  1  2  1  1 X+2  1  1  1  1  X  1  X
 0  1  0  0  1  1  1  2  1  1  3  1  X X+2  1 X+1  0  X  2 X+1 X+2  1  X  1  1  X X+3 X+1 X+1  2  0 X+1  1  2  3  1  1  2  X  1 X+2 X+2  1  1  1  X  0  1 X+2  3  X  1  0  1 X+1  X  2  1  1  2  1
 0  0  1 X+1 X+3  0 X+1  X  1  3 X+2  X  1  1 X+2  0  1  2  3 X+1 X+1 X+1  X  X  3  1  1 X+2 X+2 X+3 X+2  2 X+1  1 X+3  2  2  1  X X+3  1  0  X  3  1  3  1  3  2  0  1  1 X+3 X+1 X+2  1  2  X X+1 X+3 X+2
 0  0  0  2  0  0  0  2  2  2  0  0  0  2  2  2  2  2  2  0  0  2  0  0  2  0  2  0  2  0  2  0  2  2  0  2  2  2  0  2  0  0  2  0  0  0  2  0  0  2  0  2  2  0  0  2  2  0  0  2  0
 0  0  0  0  2  0  2  0  2  2  2  2  0  0  2  2  2  2  2  0  2  0  2  0  0  0  0  2  2  0  0  0  2  0  0  0  0  2  0  0  2  2  2  2  0  2  2  2  0  2  0  0  0  2  2  2  0  0  2  2  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  2  0  2  2  2  2  0  2  2  0  0  2  0  2  2  2  0  2  2  0  0  0  0  2  2  2  2  2  0  0  0  0  2  2  0  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+168x^55+241x^56+438x^57+276x^58+536x^59+312x^60+502x^61+293x^62+368x^63+178x^64+264x^65+107x^66+170x^67+83x^68+70x^69+27x^70+36x^71+12x^72+6x^73+1x^74+2x^75+5x^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 89.1 seconds.