The generator matrix

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

generates a code of length 84 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+68x^73+140x^74+172x^75+197x^76+254x^77+320x^78+378x^79+470x^80+570x^81+609x^82+660x^83+704x^84+634x^85+598x^86+540x^87+464x^88+358x^89+255x^90+196x^91+141x^92+118x^93+93x^94+82x^95+57x^96+42x^97+27x^98+12x^99+12x^100+2x^101+4x^102+8x^103+2x^105+1x^106+1x^108+1x^110+1x^124

The gray image is a code over GF(2) with n=336, k=13 and d=146.
This code was found by Heurico 1.16 in 11.3 seconds.