The generator matrix

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

generates a code of length 61 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+99x^56+204x^57+298x^58+224x^59+283x^60+160x^61+183x^62+138x^63+118x^64+88x^65+73x^66+40x^67+45x^68+24x^69+33x^70+14x^71+14x^72+2x^73+5x^74+2x^81

The gray image is a code over GF(2) with n=244, k=11 and d=112.
This code was found by Heurico 1.11 in 0.157 seconds.