The generator matrix

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

generates a code of length 51 over Z4 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+34x^44+58x^45+96x^46+114x^47+92x^48+88x^49+50x^50+64x^51+64x^52+48x^53+57x^54+58x^55+43x^56+34x^57+40x^58+30x^59+20x^60+10x^61+9x^62+4x^63+2x^64+2x^65+4x^66+2x^67

The gray image is a code over GF(2) with n=102, k=10 and d=44.
This code was found by Heurico 1.10 in 0.031 seconds.