The generator matrix

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

generates a code of length 75 over Z4 who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+30x^58+108x^59+248x^60+408x^61+550x^62+784x^63+1028x^64+1360x^65+1686x^66+1808x^67+2105x^68+2600x^69+2812x^70+3340x^71+3670x^72+3702x^73+4044x^74+4090x^75+4214x^76+4002x^77+3800x^78+3632x^79+3178x^80+2784x^81+2278x^82+1828x^83+1437x^84+1148x^85+896x^86+620x^87+409x^88+310x^89+246x^90+150x^91+72x^92+66x^93+38x^94+24x^95+15x^96+4x^97+4x^98+4x^100+3x^104

The gray image is a code over GF(2) with n=150, k=16 and d=58.
This code was found by Heurico 1.10 in 549 seconds.