The generator matrix

 1  0  0  1  1  1  2  1  1  1  0  2  1  0  1  1  0  1  1  1  2  0  2  1  0  1  1  2  1  0  1  1  1  0  2  2  1  2  2  1
 0  1  0  0  1  1  1  0  2  3  1  1  3  2  2  1  1  0  0  2  1  1  1  1  0  0  3  0  0  1  3  2  2  1  1  1  1  1  1  1
 0  0  1  1  1  0  1  2  3  0  2  1  3  1  0  2  2  0  2  3  3  0  2  3  1  0  1  1  2  3  0  1  2  0  0  0  1  1  1  1
 0  0  0  2  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  2  0  2  2  0  2  2  0  0  2  0  0  2  2  0  2  0  0  0  0
 0  0  0  0  2  0  0  2  2  2  2  2  0  2  0  2  0  0  2  0  0  2  0  2  2  2  0  0  0  2  0  2  2  2  0  2  0  2  2  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  2  0  2  2  0  0  2  2  0  0  2  2  2  2  2  2  2  0  2  2  2  2  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+158x^36+80x^38+114x^40+32x^42+72x^44+16x^46+21x^48+18x^52

The gray image is a code over GF(2) with n=80, k=9 and d=36.
This code was found by Heurico 1.16 in 0.0504 seconds.