The generator matrix

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

generates a code of length 72 over Z4 who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+24x^55+90x^56+212x^57+343x^58+568x^59+679x^60+998x^61+1291x^62+1430x^63+1845x^64+2320x^65+2578x^66+2906x^67+3404x^68+3610x^69+4039x^70+4164x^71+4178x^72+4138x^73+4010x^74+3904x^75+3579x^76+3134x^77+2664x^78+2338x^79+1836x^80+1472x^81+1114x^82+830x^83+606x^84+410x^85+283x^86+188x^87+136x^88+82x^89+59x^90+32x^91+28x^92+8x^93+3x^94+2x^96

The gray image is a code over GF(2) with n=144, k=16 and d=55.
This code was found by Heurico 1.10 in 359 seconds.