The generator matrix

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

generates a code of length 57 over Z4 who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+20x^41+62x^42+160x^43+367x^44+518x^45+701x^46+1024x^47+1336x^48+1670x^49+2071x^50+2432x^51+3030x^52+3688x^53+3965x^54+4414x^55+4573x^56+4746x^57+4858x^58+4488x^59+4283x^60+3800x^61+3169x^62+2576x^63+2129x^64+1742x^65+1256x^66+836x^67+552x^68+388x^69+275x^70+178x^71+105x^72+62x^73+24x^74+20x^75+8x^76+6x^77+2x^78+1x^82

The gray image is a code over GF(2) with n=114, k=16 and d=41.
This code was found by Heurico 1.10 in 396 seconds.