The generator matrix

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

generates a code of length 76 over Z4 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+212x^68+236x^70+365x^72+202x^74+270x^76+148x^78+185x^80+114x^82+142x^84+34x^86+81x^88+28x^90+24x^92+6x^94

The gray image is a code over GF(2) with n=152, k=11 and d=68.
This code was found by Heurico 1.10 in 112 seconds.