The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  0  0  0  1  1  1  1  2  2  2  2  0  0  0  2  2  2  2  2  1
 0  2  0  2  0  0  2  2  0  0  2  2  0  0  2  2  0  2  2  2  2  0  0  0  2  2  0  0  2  2  2  2  0  0  0  2  2  0  0
 0  0  2  2  0  2  2  0  0  2  2  0  0  2  2  0  2  2  0  0  2  2  0  2  2  0  0  2  2  0  0  2  2  0  2  2  0  0  0

generates a code of length 39 over Z4 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+3x^40+6x^41+4x^42+2x^45

The gray image is a code over GF(2) with n=78, k=4 and d=40.
This code was found by Heurico 1.16 in 0.00599 seconds.