The generator matrix

 1  0  0  1  1  1  2  1  0  1  1  2  X  1  1  X  1  2  2  1  1  1  1  1 X+2 X+2  X  1  1 X+2  1  X  0  1  1  2  1  1  1 X+2  1  1  1  X  1  2  0  1  1  1  1  1 X+2  1  1  X  0  0  0  1 X+2  0  1  1  X  0  X  1  0  X  2  1  1  1 X+2  1  2  X  1
 0  1  0  0  1 X+1  1 X+1  2 X+1 X+2  1  1  2  3  1  3  1  X  X  X  0 X+1 X+3  2  1  1  X  0  1 X+3 X+2  1  3  3  1 X+2  1  2  1  0  0  1  2 X+3  1 X+2  2  1  0 X+2  1  1  3  X  X  1  1  0  2  1 X+2  1  X  1  1  1  2  1  1  1 X+3  1  2  0  1  1  1  0
 0  0  1  1  1  2 X+3  3  1  2 X+3  X  1  2 X+1  2  2  3  1  X  3  X X+2 X+3  1  2  3 X+1 X+2 X+1 X+3  1  X  1 X+2 X+1  2  2 X+1 X+2  2  3  3  1  X  0  1  X X+2 X+3  3  2 X+2 X+2 X+3  1  3 X+2  1  3 X+1  1  X  1 X+2  X  1 X+3  2  3 X+3  3 X+1 X+3  1  1 X+1  2  0
 0  0  0  X X+2  0 X+2  X  X X+2  2  X  0  X  0  X X+2  0  X X+2  2  2  0  2  2  0 X+2  X X+2  X  X  2  2  2  2  0  X  2  0 X+2  2  0  X  X X+2  X  2  0  X X+2 X+2  0  0  X  X  X X+2 X+2  2  X  2  0 X+2  X  0  0  X  2  X X+2  0  0 X+2  0 X+2  2 X+2  0  0
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  2  0  0  2  2  0  0  2  0  2  2  0  2  0  2  0  0  2  2  0  0  2  0  0  0  2  0  2  2  2  0  2  2  0  2  0  0  0  0  0  2  0  2  0  0  2  0  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+52x^72+250x^73+249x^74+430x^75+327x^76+508x^77+253x^78+430x^79+203x^80+354x^81+144x^82+268x^83+115x^84+158x^85+90x^86+80x^87+57x^88+68x^89+29x^90+6x^91+8x^92+6x^93+1x^94+2x^95+3x^96+2x^98+2x^100

The gray image is a code over GF(2) with n=316, k=12 and d=144.
This code was found by Heurico 1.16 in 1.18 seconds.