The generator matrix

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

generates a code of length 84 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+89x^74+48x^75+189x^76+280x^77+216x^78+600x^79+235x^80+1032x^81+236x^82+1112x^83+216x^84+1112x^85+205x^86+1032x^87+206x^88+600x^89+186x^90+280x^91+141x^92+48x^93+63x^94+15x^96+12x^98+11x^100+11x^102+6x^104+5x^106+2x^108+1x^110+1x^112+1x^116

The gray image is a code over GF(2) with n=336, k=13 and d=148.
This code was found by Heurico 1.16 in 32.7 seconds.