The generator matrix

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

generates a code of length 72 over Z4 who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+178x^64+268x^66+321x^68+264x^70+203x^72+220x^74+165x^76+142x^78+114x^80+76x^82+58x^84+14x^86+16x^88+8x^90

The gray image is a code over GF(2) with n=144, k=11 and d=64.
This code was found by Heurico 1.10 in 0.234 seconds.