The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  X  1  2  1  1  1  1  0  1  1 X+2  1  1  X  1  0  1  1  1  1 X+2  1  0  1  1  X  1  1  2  1  1  0  0  1  1  1  1  2 X+2  1  1  X  1  1 X+2  0  1  1  1  1  1 X+2  X  X  2  X  X  X  1  1  0  1  1  1  1  1  0  1  1  2  X  2  2  1
 0  1  1 X+2 X+3  1  0 X+1  1  X  1  3  1  0 X+3  2 X+3  1  X  1  1  X  3  1 X+1  1 X+3  0  X  3  1 X+2  1  1  2  1  X  0  1  0  3  1  1 X+3 X+2  2 X+3  1  1  1 X+1  1 X+2  X  1  1  1  2  X  2 X+3  1  X  1  1  1  0  0 X+2  3  X X+1  X  1 X+3 X+3  1  X  2  X  2  1  X  0
 0  0  X  0 X+2  0 X+2  0 X+2 X+2  X  2  X  2  X  X  2  2  X  X  0  2  0 X+2  2  2  X  2 X+2 X+2  2  0  0 X+2 X+2  X X+2  0  X  2  0  0  2 X+2  0 X+2  X X+2  0  0  X  X  0  X  0 X+2 X+2 X+2  2  2  0 X+2 X+2  2  2  0 X+2  X  X  0  X  X  X  0  0 X+2  X X+2  X  X  X  0  2  0
 0  0  0  2  0  0  0  0  0  0  0  2  2  2  0  2  0  2  2  2  0  0  2  2  2  2  2  2  2  0  0  2  2  2  2  0  0  2  2  2  0  0  2  2  0  0  0  2  0  0  2  0  2  2  2  0  0  2  0  0  0  2  2  2  2  2  0  2  0  2  2  2  0  2  0  0  0  2  0  2  0  0  2  0
 0  0  0  0  2  0  0  0  0  2  2  0  2  0  0  0  2  2  2  2  2  0  2  2  0  2  0  2  2  2  2  2  0  0  2  0  2  0  2  0  0  0  2  0  2  0  2  0  0  0  0  2  0  2  2  0  0  0  2  2  0  0  0  0  2  2  2  2  0  2  2  2  0  2  2  0  2  2  0  0  0  2  2  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  2  2  2  2  0  2  0  0  2  2  0  2  0  2  2  2  2  0  0  0  0  0  2  0  0  2  0  2  0  0  2  0  2  0  0  0  0  0  2  0  0  0  2  2  2  2  2  2  2  0  2  0  2  0  2  2  2  2  2  0  2  0  2  2  2  0  0  2  0  2  0
 0  0  0  0  0  0  2  0  0  2  0  0  0  0  0  2  0  0  0  2  2  2  0  0  2  0  0  2  0  0  2  2  2  2  2  0  0  2  2  2  0  0  2  0  0  2  2  0  2  0  2  2  0  2  2  0  2  2  2  2  2  2  0  0  2  2  2  0  0  0  0  2  0  0  0  0  0  2  2  2  2  0  0  0
 0  0  0  0  0  0  0  2  0  0  0  2  0  0  0  0  2  0  2  2  2  2  0  2  2  2  2  0  0  2  2  2  2  0  0  0  0  0  0  2  2  2  0  2  2  2  0  2  2  0  2  0  0  2  2  0  0  0  2  2  0  2  0  0  0  2  0  0  0  2  2  2  0  0  2  2  2  2  2  0  0  0  2  0
 0  0  0  0  0  0  0  0  2  0  2  0  2  0  0  0  0  0  2  2  2  2  0  2  2  0  0  2  2  0  0  2  0  2  2  0  2  2  2  0  2  2  0  2  2  2  0  0  0  2  2  0  2  0  2  2  2  2  2  0  0  0  0  0  2  2  0  0  2  2  0  0  0  2  0  2  0  0  2  0  0  2  2  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+40x^72+54x^73+204x^74+268x^75+368x^76+484x^77+666x^78+792x^79+880x^80+1200x^81+1298x^82+1330x^83+1423x^84+1398x^85+1187x^86+1094x^87+972x^88+730x^89+546x^90+524x^91+304x^92+180x^93+144x^94+80x^95+75x^96+48x^97+38x^98+6x^99+23x^100+2x^101+11x^102+2x^103+8x^104+2x^106+2x^108

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 21.6 seconds.