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

generates a code of length 68 over Z4 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+42x^54+344x^56+652x^58+1114x^60+1368x^62+1718x^64+1908x^66+2105x^68+1964x^70+1732x^72+1422x^74+966x^76+568x^78+291x^80+128x^82+46x^84+10x^86+2x^88+2x^90+1x^100

The gray image is a code over GF(2) with n=136, k=14 and d=54.
This code was found by Heurico 1.10 in 14.4 seconds.