The generator matrix

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

generates a code of length 84 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+151x^72+20x^73+94x^74+152x^75+388x^76+504x^77+278x^78+1220x^79+557x^80+1736x^81+396x^82+2512x^83+471x^84+2512x^85+396x^86+1736x^87+494x^88+1220x^89+278x^90+504x^91+312x^92+152x^93+94x^94+20x^95+109x^96+36x^100+31x^104+8x^108+1x^112+1x^116

The gray image is a code over GF(2) with n=336, k=14 and d=144.
This code was found by Heurico 1.16 in 21.9 seconds.