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

generates a code of length 91 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+58x^78+4x^79+160x^80+28x^81+264x^82+108x^83+325x^84+292x^85+406x^86+464x^87+465x^88+664x^89+433x^90+920x^91+424x^92+776x^93+410x^94+420x^95+387x^96+268x^97+302x^98+124x^99+203x^100+20x^101+121x^102+8x^103+45x^104+37x^106+20x^108+10x^110+14x^112+4x^114+2x^116+3x^118+2x^124

The gray image is a code over GF(2) with n=364, k=13 and d=156.
This code was found by Heurico 1.16 in 11.1 seconds.