The generator matrix

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

generates a code of length 68 over Z4 who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+26x^53+116x^54+260x^55+366x^56+484x^57+655x^58+766x^59+911x^60+1180x^61+1453x^62+1528x^63+1578x^64+1806x^65+2051x^66+2052x^67+2041x^68+2054x^69+2134x^70+1952x^71+1668x^72+1676x^73+1505x^74+1242x^75+807x^76+732x^77+617x^78+316x^79+265x^80+210x^81+145x^82+68x^83+40x^84+24x^85+24x^86+8x^87+1x^88+4x^90+1x^100+1x^104

The gray image is a code over GF(2) with n=136, k=15 and d=53.
This code was found by Heurico 1.10 in 164 seconds.