The generator matrix

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

generates a code of length 41 over Z4 who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+18x^27+99x^28+224x^29+398x^30+670x^31+877x^32+1322x^33+1896x^34+2364x^35+3042x^36+3848x^37+4434x^38+4964x^39+5641x^40+5696x^41+5484x^42+5202x^43+4679x^44+4032x^45+3146x^46+2302x^47+1636x^48+1306x^49+904x^50+544x^51+388x^52+200x^53+118x^54+64x^55+21x^56+12x^57+4x^58

The gray image is a code over GF(2) with n=82, k=16 and d=27.
This code was found by Heurico 1.10 in 98.9 seconds.