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

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+38x^72+42x^73+111x^74+162x^75+241x^76+304x^77+315x^78+400x^79+428x^80+546x^81+616x^82+612x^83+683x^84+614x^85+609x^86+584x^87+436x^88+368x^89+244x^90+226x^91+152x^92+132x^93+110x^94+56x^95+43x^96+34x^97+26x^98+8x^99+19x^100+6x^101+13x^102+6x^104+2x^105+1x^106+1x^108+1x^110+2x^114

The gray image is a code over GF(2) with n=336, k=13 and d=144.
This code was found by Heurico 1.16 in 8.29 seconds.