The generator matrix

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

generates a code of length 70 over Z4 who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+48x^53+112x^54+228x^55+418x^56+540x^57+702x^58+1036x^59+1296x^60+1492x^61+1805x^62+2226x^63+2658x^64+2996x^65+3237x^66+3606x^67+3930x^68+4116x^69+4159x^70+4140x^71+4098x^72+3738x^73+3552x^74+3094x^75+2666x^76+2372x^77+1762x^78+1516x^79+1206x^80+842x^81+637x^82+442x^83+310x^84+196x^85+143x^86+80x^87+48x^88+42x^89+16x^90+14x^91+6x^92+3x^94+2x^95+3x^96+2x^97

The gray image is a code over GF(2) with n=140, k=16 and d=53.
This code was found by Heurico 1.10 in 500 seconds.