The generator matrix

 1  0  0  0  1  1  1  2  1  1  1  2  1  0  X  1  1  1  1 X+2  1  0 X+2  2  X  2  1  1 X+2  1  X  0  1 X+2  1  1  X  2  1  0  0  1  0  1  X  1  1 X+2  1  1  1  1  1  1  1  X X+2  1  0  1  1  1  X  0  2  1  1  0  1 X+2 X+2  1  1  1  1  0  2  0 X+2
 0  1  0  0  X  X X+2  0  1  3  3  1 X+3  1  1  X  0 X+3 X+2  0  3  2  1  X  1  1 X+3  1  1  0  1  1 X+3  1  2  1  2  1 X+3  1  0 X+2  1 X+2  X  3 X+3  1  2 X+2  1  X  3  X X+1  1  1  0  X  3  3  3  1  1  1 X+2  2  1  0  1  2  2  1  X  0  1  X  1  0
 0  0  1  0  X X+3 X+3  1 X+1 X+2  2  1 X+1  3  X  0  3  0  2  1  1  1  1  0 X+3  2  3 X+2  2  1 X+1 X+2  X X+1 X+3  1  1 X+1 X+3  1  1  3  X X+1  X  X X+1  3  3  0  0 X+3 X+3  X X+3  2  1  2  1 X+2 X+1  3 X+3  2 X+3  0  0 X+1 X+2  3  1  X  2 X+2  X  X  1 X+3  2
 0  0  0  1 X+1 X+3  X  3  X X+2  3  1 X+3  X X+3  X  2  3  1  X  X X+3  3  1  0 X+2 X+1  2 X+3  1  X  2  0 X+1  3 X+1 X+1  2  2  3  0  X X+2 X+1  1  1  X  2 X+2  0 X+2  1  2 X+2 X+3 X+2 X+1 X+2  3 X+1  1 X+2 X+1 X+1  0  0 X+1  3  1  X  2  X  3 X+3  2 X+3  2 X+1  1
 0  0  0  0  2  2  2  0  2  2  2  0  2  0  0  2  2  2  2  0  2  0  0  0  0  0  2  2  0  2  0  0  2  0  2  0  2  2  0  2  2  0  2  0  2  0  0  2  0  0  0  0  0  0  0  2  2  0  2  0  0  0  2  2  0  2  0  2  0  2  2  2  0  0  0  0  2  2  0

generates a code of length 79 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+446x^72+1162x^74+1466x^76+1384x^78+1196x^80+1002x^82+659x^84+476x^86+259x^88+104x^90+35x^92+2x^96

The gray image is a code over GF(2) with n=316, k=13 and d=144.
This code was found by Heurico 1.16 in 60.8 seconds.