The generator matrix

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

generates a code of length 40 over Z4 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+12x^42+2x^44+1x^48

The gray image is a code over GF(2) with n=80, k=4 and d=42.
This code was found by Heurico 1.16 in 0.00923 seconds.