The generator matrix

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

generates a code of length 53 over Z4 who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+46x^38+136x^39+210x^40+422x^41+675x^42+948x^43+1271x^44+1600x^45+2082x^46+2546x^47+3027x^48+3682x^49+4068x^50+4372x^51+4930x^52+4950x^53+4758x^54+4816x^55+4467x^56+3810x^57+3171x^58+2578x^59+2111x^60+1546x^61+1052x^62+830x^63+556x^64+322x^65+234x^66+148x^67+64x^68+46x^69+36x^70+8x^71+3x^72+4x^73+4x^74+2x^75+2x^77+2x^78

The gray image is a code over GF(2) with n=106, k=16 and d=38.
This code was found by Heurico 1.10 in 152 seconds.