The generator matrix

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

generates a code of length 40 over Z4 who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+46x^29+138x^30+214x^31+397x^32+536x^33+656x^34+806x^35+903x^36+1108x^37+1246x^38+1330x^39+1420x^40+1354x^41+1346x^42+1236x^43+1035x^44+886x^45+574x^46+450x^47+290x^48+156x^49+124x^50+54x^51+45x^52+8x^53+10x^54+6x^55+4x^56+2x^57+2x^58+1x^60

The gray image is a code over GF(2) with n=80, k=14 and d=29.
This code was found by Heurico 1.16 in 32.7 seconds.