The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+55x^36+56x^38+61x^40+34x^42+29x^44+4x^46+8x^48+2x^50+4x^52+2x^56

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 0.0132 seconds.