The generator matrix

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

generates a code of length 68 over Z4 who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+56x^55+148x^56+248x^57+357x^58+446x^59+552x^60+638x^61+764x^62+794x^63+866x^64+848x^65+944x^66+980x^67+953x^68+1098x^69+938x^70+964x^71+906x^72+840x^73+741x^74+606x^75+510x^76+338x^77+304x^78+234x^79+143x^80+80x^81+46x^82+16x^83+16x^84+6x^85+2x^86+1x^116

The gray image is a code over GF(2) with n=136, k=14 and d=55.
This code was found by Heurico 1.10 in 14.7 seconds.