The generator matrix

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

generates a code of length 40 over Z4 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+81x^28+138x^29+424x^30+428x^31+777x^32+898x^33+1268x^34+1510x^35+1853x^36+2226x^37+2274x^38+2920x^39+2758x^40+2980x^41+2618x^42+2352x^43+1923x^44+1610x^45+1268x^46+832x^47+666x^48+310x^49+304x^50+138x^51+127x^52+26x^53+34x^54+12x^55+6x^56+4x^57+2x^58

The gray image is a code over GF(2) with n=80, k=15 and d=28.
This code was found by Heurico 1.16 in 67.8 seconds.