The generator matrix

 1  0  0  1  1  1  0  1  1  1  X  2  1  2 X+2  0  1  1  1  X  1  1 X+2  1  2  1  X  1  X  1  1  1  2  1  2  0  1  0  1 X+2  1  1  1  X  1  1  X  2  1  1 X+2  1  1  1 X+2 X+2  1 X+2  1  1  0  0  0  1  2  1  1 X+2  1  X  1  2  X  1  1  2  1  1  1
 0  1  0  0  1  1  1  2 X+3 X+1  1  1  X X+2  1  1 X+3  3  X  2 X+2 X+1  1 X+2  2  3  1  X  X  0  2  1  1  X  1  1  3  1  3  1 X+3  2  2 X+2 X+1  1  1  1 X+2 X+3  1  0  2 X+2  1  1 X+2  1  1  2  1 X+2  1  3  2  1 X+3  1 X+1  1  1  1  1  X X+1  1  3 X+1  0
 0  0  1 X+1 X+3  0 X+1  X X+2 X+3  1  X  1  1 X+2  1  3 X+2  2  1 X+3  0  2  1  1  3 X+1 X+2  1  1  2  X  0  2  3 X+2  0  1 X+3 X+1 X+2 X+1 X+3  1 X+3 X+3  0 X+3  X X+3  3 X+2  X X+3  0 X+2  3  1  0 X+2  1  1  3  2  1  0  X  0  1 X+2  X X+2  0  3 X+1  2  1  1  0
 0  0  0  2  0  0  0  2  2  2  0  0  0  2  2  2  0  0  0  2  2  0  2  0  0  0  2  2  2  2  0  2  2  2  0  0  2  2  0  0  0  2  0  0  2  2  0  2  0  2  0  0  2  0  0  2  0  2  2  0  2  2  0  2  2  2  2  0  2  2  2  2  2  2  2  0  2  0  2
 0  0  0  0  2  0  2  0  0  0  0  2  0  0  0  0  0  0  2  2  2  2  2  2  2  0  2  2  0  2  2  0  0  0  2  2  2  0  2  0  2  0  0  0  0  2  0  2  2  2  0  0  2  0  2  2  2  0  0  0  2  2  0  0  0  2  2  2  0  2  2  2  0  0  0  2  0  0  2
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  0  2  2  2  2  0  2  2  2  2  2  2  0  2  2  2  0  0  0  2  2  2  2  0  2  2  0  0  0  2  2  0  0  0  0  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+40x^72+296x^73+146x^74+558x^75+204x^76+582x^77+198x^78+500x^79+132x^80+422x^81+106x^82+310x^83+85x^84+184x^85+40x^86+148x^87+46x^88+46x^89+16x^90+16x^91+2x^92+6x^93+6x^94+4x^95+1x^96+1x^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 1.11 seconds.