The generator matrix

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

generates a code of length 53 over Z4 who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+62x^45+94x^46+124x^47+161x^48+140x^49+155x^50+176x^51+163x^52+130x^53+96x^54+100x^55+117x^56+94x^57+96x^58+76x^59+75x^60+72x^61+30x^62+32x^63+25x^64+14x^65+9x^66+4x^67+2x^68

The gray image is a code over GF(2) with n=106, k=11 and d=45.
This code was found by Heurico 1.10 in 0.172 seconds.