The generator matrix

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

generates a code of length 79 over Z4 who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+41x^70+78x^71+137x^72+170x^73+148x^74+146x^75+111x^76+134x^77+132x^78+120x^79+95x^80+82x^81+83x^82+84x^83+94x^84+66x^85+60x^86+54x^87+41x^88+30x^89+41x^90+20x^91+31x^92+20x^93+5x^94+8x^95+2x^96+10x^97+2x^99+2x^102

The gray image is a code over GF(2) with n=158, k=11 and d=70.
This code was found by Heurico 1.10 in 0.25 seconds.