The generator matrix

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

generates a code of length 40 over Z4 who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+190x^36+190x^40+76x^44+41x^48+14x^52

The gray image is a code over GF(2) with n=80, k=9 and d=36.
This code was found by Heurico 1.10 in 74.4 seconds.