The generator matrix

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

generates a code of length 73 over Z4 who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+26x^57+72x^58+154x^59+265x^60+372x^61+550x^62+710x^63+833x^64+962x^65+1198x^66+1272x^67+1384x^68+1702x^69+1869x^70+1902x^71+1885x^72+2034x^73+2063x^74+2004x^75+1932x^76+1768x^77+1656x^78+1398x^79+1120x^80+974x^81+746x^82+584x^83+416x^84+294x^85+246x^86+146x^87+73x^88+52x^89+39x^90+18x^91+27x^92+8x^93+6x^94+4x^95+2x^98+1x^102

The gray image is a code over GF(2) with n=146, k=15 and d=57.
This code was found by Heurico 1.10 in 119 seconds.