The generator matrix

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

generates a code of length 40 over Z4 who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+24x^37+22x^38+16x^39+22x^40+8x^41+8x^42+8x^44+16x^45+2x^46+1x^64

The gray image is a code over GF(2) with n=80, k=7 and d=37.
This code was found by Heurico 1.16 in 0.0701 seconds.