The generator matrix

1 0 0 0 0 1 1 1 1 2 1 2 1 0 0 1 2 1 2 1 1 1 2 0 0 1 1 0 1 0 1 2 1 2 2 1 1 1 1 2 0 0 0 2 1 1 0 1 1 1 1 2 0 0 1 1 0 0 1 1 0
0 1 0 0 0 0 0 0 2 0 0 2 2 0 1 1 1 3 1 3 1 3 1 1 1 3 1 1 3 0 2 1 1 1 1 2 2 0 1 1 2 0 1 2 0 2 0 0 1 2 2 1 2 1 2 1 2 1 3 1 1
0 0 1 0 0 0 0 1 1 1 2 1 1 2 1 2 3 0 0 1 2 1 0 2 1 2 1 1 1 1 1 1 3 3 0 3 2 1 3 1 1 0 2 0 2 2 1 3 1 3 0 2 0 0 0 1 1 3 2 0 0
0 0 0 1 0 1 0 2 1 1 1 1 3 1 0 3 1 3 3 2 0 0 2 1 2 2 3 1 1 2 2 1 2 3 2 1 2 0 2 0 1 1 0 0 0 1 1 1 0 3 3 3 1 0 0 0 3 1 1 0 3
0 0 0 0 1 1 3 3 1 0 2 3 2 1 3 1 1 2 2 0 3 1 3 3 2 2 0 0 1 1 2 2 1 1 3 3 3 3 2 3 3 2 0 1 2 0 0 1 1 2 3 1 2 1 0 2 3 2 2 3 0
0 0 0 0 0 2 2 2 2 0 0 2 0 2 2 2 2 0 0 0 2 2 2 2 0 0 0 0 0 0 2 2 0 0 0 0 0 0 2 0 0 2 2 2 2 2 2 0 2 2 0 0 2 2 2 0 0 2 2 0 2

generates a code of length 61 over Z4 who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+66x^53+114x^54+144x^55+173x^56+148x^57+142x^58+148x^59+141x^60+116x^61+116x^62+106x^63+84x^64+90x^65+92x^66+76x^67+75x^68+68x^69+44x^70+34x^71+26x^72+20x^73+2x^74+4x^75+8x^76+2x^77+2x^78+4x^80+2x^81

The gray image is a code over GF(2) with n=122, k=11 and d=53.
This code was found by Heurico 1.10 in 0.266 seconds.