The generator matrix

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

generates a code of length 54 over Z4 who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+76x^41+218x^42+380x^43+437x^44+656x^45+897x^46+1044x^47+1372x^48+1506x^49+1778x^50+2014x^51+2158x^52+2500x^53+2470x^54+2406x^55+2377x^56+2110x^57+1842x^58+1660x^59+1449x^60+1056x^61+805x^62+570x^63+325x^64+252x^65+150x^66+112x^67+68x^68+34x^69+28x^70+4x^71+5x^72+4x^74+2x^75+2x^77

The gray image is a code over GF(2) with n=108, k=15 and d=41.
This code was found by Heurico 1.10 in 43.2 seconds.