The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+68x^36+56x^38+34x^40+32x^42+43x^44+8x^46+11x^48+2x^56+1x^60

The gray image is a code over GF(2) with n=80, k=8 and d=36.
This code was found by Heurico 1.16 in 0.029 seconds.