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

generates a code of length 83 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+156x^72+52x^73+262x^74+340x^75+363x^76+888x^77+444x^78+1552x^79+425x^80+2240x^81+478x^82+2384x^83+439x^84+1960x^85+436x^86+1512x^87+356x^88+908x^89+270x^90+348x^91+207x^92+96x^93+128x^94+8x^95+61x^96+30x^98+29x^100+8x^104+2x^108+1x^112

The gray image is a code over GF(2) with n=332, k=14 and d=144.
This code was found by Heurico 1.16 in 20.9 seconds.