The generator matrix

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

generates a code of length 89 over Z4 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+34x^78+100x^79+167x^80+216x^81+242x^82+244x^83+243x^84+214x^85+192x^86+238x^87+203x^88+178x^89+215x^90+216x^91+150x^92+176x^93+184x^94+140x^95+150x^96+100x^97+112x^98+98x^99+77x^100+66x^101+38x^102+32x^103+23x^104+10x^105+5x^106+18x^107+10x^108+2x^111+2x^114

The gray image is a code over GF(2) with n=178, k=12 and d=78.
This code was found by Heurico 1.10 in 1.17 seconds.