The generator matrix

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

generates a code of length 88 over Z4 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+218x^78+380x^80+452x^82+532x^84+444x^86+391x^88+376x^90+333x^92+306x^94+245x^96+164x^98+118x^100+72x^102+39x^104+16x^106+9x^108

The gray image is a code over GF(2) with n=176, k=12 and d=78.
This code was found by Heurico 1.10 in 224 seconds.