The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  1  X  1  1  X  0  1  1  X  1  1  1  X  1  1  2  1  1  1  1  X  1  2  1  0  1  1  2  1  1  1  2  1  2  1  1  1  1  1  1  1  1  1  2  2  1 X+2  X  1  1  X  1 X+2  1  1  0 X+2  X  1  1  1  1  2  2  0  1  2  1  0
 0  1  1  0 X+3  1 X+1 X+2  1  2  3  1  X X+3  1  1 X+3 X+2  1  3  X X+1  1  0  3  1 X+2  3  2  X  1 X+1  1  X  1 X+1 X+3  1 X+1  0  0  1  2  1  3  X X+1  2 X+3  X  X  0 X+2  1  1  0  1  1  0 X+3  1  3  1 X+3 X+3  1  1  1 X+3  1 X+2  1  1  1  1  1  1 X+1  X
 0  0  X  0 X+2  0  2  2  X X+2  0 X+2 X+2  2  0 X+2 X+2 X+2  X  2  0  X  2 X+2 X+2  2  2 X+2  0  2 X+2  0 X+2  X  0  X  2  X  2 X+2  2  X  X  0 X+2  X  2  0  2 X+2  X  2  X  X  X  2  2  2  X  0 X+2  X  2  0  X  2  2  X  X  2  2  0  2  X  X  X  X  0 X+2
 0  0  0  X  0  0  0  2  2  2  2  0  2 X+2 X+2  X  X X+2  X X+2 X+2  X X+2 X+2 X+2 X+2  0  2 X+2 X+2  2  0  0  X  2 X+2  X X+2 X+2  X X+2  X  2  2  2  0  0  2  2 X+2  0 X+2  2  0  X  0  0  2  X X+2 X+2  X  0  2 X+2  2  X  0  2 X+2  0  0 X+2 X+2  2  2 X+2  X  0
 0  0  0  0  2  0  0  0  2  2  0  2  2  0  0  2  2  2  2  0  0  2  0  0  0  2  2  0  2  2  0  2  0  0  2  0  2  0  2  0  2  0  0  2  2  2  0  2  2  2  2  0  0  2  2  2  2  2  0  0  0  0  2  2  0  0  2  2  2  2  2  2  0  0  0  0  2  0  0
 0  0  0  0  0  2  2  2  0  2  0  2  0  0  2  0  2  0  2  2  2  0  0  0  2  0  0  2  0  2  0  0  2  2  0  0  2  0  0  0  2  2  2  2  2  0  0  2  2  2  2  2  0  2  2  0  2  0  2  0  0  0  0  0  2  2  2  0  2  0  2  0  0  2  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+187x^72+136x^73+365x^74+268x^75+410x^76+244x^77+393x^78+232x^79+329x^80+272x^81+397x^82+252x^83+293x^84+116x^85+87x^86+16x^87+30x^88+26x^90+15x^92+8x^94+8x^96+4x^98+5x^100+1x^104+1x^108

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 1.4 seconds.