The generator matrix

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

generates a code of length 72 over Z4 who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+136x^62+350x^64+462x^66+513x^68+480x^70+492x^72+344x^74+408x^76+360x^78+233x^80+154x^82+103x^84+40x^86+12x^88+8x^90

The gray image is a code over GF(2) with n=144, k=12 and d=62.
This code was found by Heurico 1.16 in 2.6 seconds.